-
1
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
2
-
-
85008014734
-
Handbook of Mathematical Functions, 2nd printing with corrections. National Bureau of Standards, Washington (1964); republished by Dover
-
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions, 2nd printing with corrections. National Bureau of Standards, Washington (1964); republished by Dover, New York (1965)
-
(1965)
New York
-
-
Abramowitz, M.1
Stegun, I.A.2
-
4
-
-
77949264980
-
A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions
-
Agarwal, R.P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109, 973–1033 (2010)
-
(2010)
Acta Appl. Math.
, vol.109
, pp. 973-1033
-
-
Agarwal, R.P.1
Benchohra, M.2
Hamani, S.3
-
5
-
-
33947164737
-
Fractional-order dynamical models of love
-
Ahmad, W.M., El-Khazali, R.: Fractional-order dynamical models of love. Chaos Solitons Fractals 33, 1367–1375 (2007)
-
(2007)
Chaos Solitons Fractals
, vol.33
, pp. 1367-1375
-
-
Ahmad, W.M.1
El-Khazali, R.2
-
6
-
-
0010999805
-
Einführung in die Theorie der Gammafunktion. Teubner
-
English translation: The Gamma Function. Holt, Rinehart and Winston, New York
-
Artin, E.: Einführung in die Theorie der Gammafunktion. Teubner, Leipzig (1931); English translation: The Gamma Function. Holt, Rinehart and Winston, New York (1964)
-
(1964)
Leipzig
, vol.1931
-
-
Artin, E.1
-
7
-
-
4043057005
-
An asymptotic fractional differential model of spherical flame
-
Matignon, D., Montseny, G. (eds.), pp., SMAI, Paris
-
Audounet, J., Roquejoffre, J.-M.: An asymptotic fractional differential model of spherical flame. In: Matignon, D., Montseny, G. (eds.) Fractional Differential Systems: Models, Methods and Applications, pp. 15–27. SMAI, Paris (1998)
-
(1998)
Fractional Differential Systems: Models, Methods and Applications
, pp. 15-27
-
-
Audounet, J.1
Roquejoffre, J.-M.2
-
8
-
-
0009933441
-
A threshold phenomenon in the propagation of a point source initiated flame
-
Audounet, J., Giovangigli, V., Roquejoffre, J.-M.: A threshold phenomenon in the propagation of a point source initiated flame. Physica D 121, 295–316 (1998)
-
(1998)
Physica D
, vol.121
, pp. 295-316
-
-
Audounet, J.1
Giovangigli, V.2
Roquejoffre, J.-M.3
-
9
-
-
0026124343
-
Fractional order state equations for the control of viscoelastically damped structures
-
Bagley, R.L., Calico, R.A.: Fractional order state equations for the control of viscoelastically damped structures. J. Guid. Contr. Dynam. 14, 304–311 (1991)
-
(1991)
J. Guid. Contr. Dynam.
, vol.14
, pp. 304-311
-
-
Bagley, R.L.1
Calico, R.A.2
-
10
-
-
0001342751
-
On the existence of the order domain and the solution of distributed order equations – Part I
-
Bagley, R.L., Torvik, P.J.: On the existence of the order domain and the solution of distributed order equations – Part I. Int. J. Appl. Math. 2, 865–882 (2000)
-
(2000)
Int. J. Appl. Math.
, vol.2
, pp. 865-882
-
-
Bagley, R.L.1
Torvik, P.J.2
-
11
-
-
0001342751
-
On the existence of the order domain and the solution of distributed order equations – Part II
-
Bagley, R.L., Torvik, P.J.: On the existence of the order domain and the solution of distributed order equations – Part II. Int. J. Appl. Math. 2, 965–987 (2000)
-
(2000)
Int. J. Appl. Math.
, vol.2
, pp. 965-987
-
-
Bagley, R.L.1
Torvik, P.J.2
-
12
-
-
34648831966
-
Fractional-order anisotropic diffusion for image denoising
-
Bai, J., Feng, X.-C.: Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Process. 16, 2492–2502 (2007)
-
(2007)
IEEE Trans. Image Process.
, vol.16
, pp. 2492-2502
-
-
Bai, J.1
Feng, X.-C.2
-
13
-
-
65049084831
-
-
World Scientific, Singapore
-
Baleanu, D., Diethelm, K., Scalas, E., Trujillo, J.J.: Fractional Calculus: Models and Numerical Methods. World Scientific, Singapore (2012)
-
(2012)
Fractional Calculus: Models and Numerical Methods
-
-
Baleanu, D.1
Diethelm, K.2
Scalas, E.3
Trujillo, J.J.4
-
14
-
-
0002502625
-
On the motion of a sphere in a viscous liquid
-
Basset, A.B.: On the motion of a sphere in a viscous liquid. Philos. Trans. R. Soc. A 179, 43–63 (1888)
-
(1888)
Philos. Trans. R. Soc. A
, vol.179
, pp. 43-63
-
-
Basset, A.B.1
-
15
-
-
0345432546
-
On the descent of a sphere in a viscous liquid
-
Basset, A.B.: On the descent of a sphere in a viscous liquid. Q. J. Pure Appl. Math. 41, 369–381 (1910)
-
(1910)
Q. J. Pure Appl. Math.
, vol.41
, pp. 369-381
-
-
Basset, A.B.1
-
16
-
-
58249103422
-
Boundary value problems for differential equations with fractional order
-
Benchohra, M., Hamani, S., Ntouyas, S.K.: Boundary value problems for differential equations with fractional order. Surv. Math. Appl. 3, 1–12 (2008)
-
(2008)
Surv. Math. Appl.
, vol.3
, pp. 1-12
-
-
Benchohra, M.1
Hamani, S.2
Ntouyas, S.K.3
-
18
-
-
34247394106
-
On systems of linear fractional differential equations with constant coefficients
-
Bonilla, B., Rivero, M., Trujillo, J.J.: On systems of linear fractional differential equations with constant coefficients. Appl. Math. Comput. 187, 68–78 (2007)
-
(2007)
Appl. Math. Comput.
, vol.187
, pp. 68-78
-
-
Bonilla, B.1
Rivero, M.2
Trujillo, J.J.3
-
19
-
-
0003855437
-
-
Vandenhoeck & Ruprecht, Göttingen
-
Braß, H.: Quadraturverfahren. Vandenhoeck & Ruprecht, Göttingen (1977)
-
(1977)
Quadraturverfahren
-
-
Braß, H.1
-
21
-
-
0040575075
-
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
-
Brunner, H., Pedas, A., Vainikko, G.: The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Math. Comput. 68, 1079–1095 (1999)
-
(1999)
Math. Comput.
, vol.68
, pp. 1079-1095
-
-
Brunner, H.1
Pedas, A.2
Vainikko, G.3
-
22
-
-
85067857168
-
-
World Scientific, River Edge, NJ
-
Caponetto, R., Dongola, G., Fortuna, L., Petráš, I.: Fractional Order Systems: Modeling and Control Applications. World Scientific, River Edge, NJ (2010)
-
(2010)
Fractional Order Systems: Modeling and Control Applications
-
-
Caponetto, R.1
Dongola, G.2
Fortuna, L.3
Petráš, I.4
-
23
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
24
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
25
-
-
51649182765
-
Linear models of dissipation in anelastic solids
-
Caputo, M., Mainardi, F.: Linear models of dissipation in anelastic solids. Rivista del Nuovo Cimento 1, 161–198 (1971)
-
(1971)
Rivista Del Nuovo Cimento
, vol.1
, pp. 161-198
-
-
Caputo, M.1
Mainardi, F.2
-
26
-
-
18444384521
-
Statistical origins of fractional derivatives in viscoelasticity
-
Chatterjee, A.: Statistical origins of fractional derivatives in viscoelasticity. J. Sound Vib. 284, 1239–1245 (2005)
-
(2005)
J. Sound Vib.
, vol.284
, pp. 1239-1245
-
-
Chatterjee, A.1
-
27
-
-
34249883566
-
The final value theorem revisited – infinite limits and irrational functions
-
Chen, J., Lundberg, K.H., Davison, D.E., Bernstein, D.S.: The final value theorem revisited – infinite limits and irrational functions. IEEE Contr. Syst. Mag. 27 (3), 97–99 (2007)
-
(2007)
IEEE Contr. Syst. Mag.
, vol.27
, Issue.3
, pp. 97-99
-
-
Chen, J.1
Lundberg, K.H.2
Davison, D.E.3
Bernstein, D.S.4
-
31
-
-
79959753668
-
Image processing by means of a linear integro-differential equation
-
Hamza, M.H. (ed.), ACTA Press, Calgary
-
Cuesta, E., Finat Codes, J.: Image processing by means of a linear integro-differential equation. In: Hamza, M.H. (ed.) Visualization, Imaging, and Image Processing 2003, Paper 91. ACTA Press, Calgary (2003)
-
(2003)
Visualization, Imaging, and Image Processing 2003, Paper
, pp. 91
-
-
Cuesta, E.1
Finat Codes, J.2
-
32
-
-
84966251516
-
Asymptotic expansions for product integration
-
de Hoog, F., Weiss, R.: Asymptotic expansions for product integration. Math. Comput. 27, 295–306 (1973)
-
(1973)
Math. Comput.
, vol.27
, pp. 295-306
-
-
de Hoog, F.1
Weiss, R.2
-
33
-
-
34249335010
-
Short memory principle and a predictor-corrector approach for fractional differential equations
-
Deng, W.: Short memory principle and a predictor-corrector approach for fractional differential equations. J. Comput. Appl. Math. 206, 174–188 (2007)
-
(2007)
J. Comput. Appl. Math.
, vol.206
, pp. 174-188
-
-
Deng, W.1
-
34
-
-
0001618393
-
An algorithm for the numerical solution of differential equations of fractional order
-
Diethelm, K.: An algorithm for the numerical solution of differential equations of fractional order. Electron. Trans. Numer. Anal. 5, 1–6 (1997)
-
(1997)
Electron. Trans. Numer. Anal.
, vol.5
, pp. 1-6
-
-
Diethelm, K.1
-
35
-
-
30444454946
-
Predictor-corrector strategies for single-and multi-term fractional differential equations
-
Lipitakis, E.A. (ed.), pp., LEA Press, Athens
-
Diethelm, K.: Predictor-corrector strategies for single-and multi-term fractional differential equations. In: Lipitakis, E.A. (ed.) Proceedings of the 5th Hellenic-European Conference on Computer Mathematics and Its Applications, pp. 117–122. LEA Press, Athens (2002)
-
(2002)
Proceedings of the 5Th Hellenic-European Conference on Computer Mathematics and Its Applications
, pp. 117-122
-
-
Diethelm, K.1
-
36
-
-
0348158242
-
mE methods
-
mE methods. Computing 71, 305–319 (2003)
-
(2003)
Computing
, vol.71
, pp. 305-319
-
-
Diethelm, K.1
-
37
-
-
77956152726
-
Smoothness properties of solutions of Caputo-type fractional differential equations
-
Diethelm, K.: Smoothness properties of solutions of Caputo-type fractional differential equations. Fract. Calc. Appl. Anal. 10, 151–160 (2007)
-
(2007)
Fract. Calc. Appl. Anal.
, vol.10
, pp. 151-160
-
-
Diethelm, K.1
-
38
-
-
42149141688
-
An investigation of some nonclassical methods for the numerical approximation of Caputo-type fractional derivatives
-
Diethelm, K.: An investigation of some nonclassical methods for the numerical approximation of Caputo-type fractional derivatives. Numer. Algorithms 47, 361–390 (2008)
-
(2008)
Numer. Algorithms
, vol.47
, pp. 361-390
-
-
Diethelm, K.1
-
39
-
-
70450163815
-
Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution
-
Diethelm, K.: Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution. J. Eur. Syst. Autom. 42, 665–676 (2008)
-
(2008)
J. Eur. Syst. Autom.
, vol.42
, pp. 665-676
-
-
Diethelm, K.1
-
40
-
-
77956153293
-
On the separation of solutions of fractional differential equations
-
Diethelm, K.: On the separation of solutions of fractional differential equations. Fract. Calc. Appl. Anal. 11, 259–268 (2008)
-
(2008)
Fract. Calc. Appl. Anal.
, vol.11
, pp. 259-268
-
-
Diethelm, K.1
-
41
-
-
76049087706
-
An improvement of a nonclassical numerical method for the computation of fractional derivatives
-
Diethelm, K.: An improvement of a nonclassical numerical method for the computation of fractional derivatives. J. Vib. Acoust. 131, 014502 (2009)
-
(2009)
J. Vib. Acoust.
, vol.131
-
-
Diethelm, K.1
-
42
-
-
0012570827
-
Numerical solution methods for distributed order differential equations
-
Diethelm, K., Ford, N.J.: Numerical solution methods for distributed order differential equations. Fract. Calc. Appl. Anal. 4, 531–542 (2001)
-
(2001)
Fract. Calc. Appl. Anal.
, vol.4
, pp. 531-542
-
-
Diethelm, K.1
Ford, N.J.2
-
43
-
-
0037081673
-
Analysis of fractional differential equations
-
Diethelm, K., Ford, N.J.: Analysis of fractional differential equations. J. Math. Anal. Appl. 265, 229–248 (2002)
-
(2002)
J. Math. Anal. Appl.
, vol.265
, pp. 229-248
-
-
Diethelm, K.1
Ford, N.J.2
-
44
-
-
0012899160
-
Numerical solution of the Bagley–Torvik equation
-
Diethelm, K., Ford, N.J.: Numerical solution of the Bagley–Torvik equation. BIT 42, 490–507 (2002)
-
(2002)
BIT
, vol.42
, pp. 490-507
-
-
Diethelm, K.1
Ford, N.J.2
-
45
-
-
3042709180
-
Multi-order fractional differential equations and their numerical solution
-
Diethelm, K., Ford, N.J.: Multi-order fractional differential equations and their numerical solution. Appl. Math. Comput. 154, 621–640 (2004)
-
(2004)
Appl. Math. Comput.
, vol.154
, pp. 621-640
-
-
Diethelm, K.1
Ford, N.J.2
-
46
-
-
58549120748
-
Numerical analysis for distributed order differential equations
-
Diethelm, K., Ford, N.J.: Numerical analysis for distributed order differential equations. J. Comput. Appl. Math. 225, 96–104 (2009)
-
(2009)
J. Comput. Appl. Math.
, vol.225
, pp. 96-104
-
-
Diethelm, K.1
Ford, N.J.2
-
47
-
-
85009408983
-
Volterra integral equations and fractional calculus: Do neighbouring solutions intersect?
-
in press
-
Diethelm, K., Ford, N.J.: Volterra integral equations and fractional calculus: do neighbouring solutions intersect? J. Integr. Equ. Appl. (in press)
-
J. Integr. Equ. Appl.
-
-
Diethelm, K.1
Ford, N.J.2
-
48
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equations
-
Diethelm, K., Ford, N.J., Freed, A.D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam. 29, 3–22 (2002)
-
(2002)
Nonlinear Dynam
, vol.29
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
49
-
-
4043121080
-
Detailed error analysis for a fractional Adams method
-
Diethelm, K., Ford, N.J., Freed A.D.: Detailed error analysis for a fractional Adams method. Numer. Algorithms 36, 31–52 (2004)
-
(2004)
Numer. Algorithms
, vol.36
, pp. 31-52
-
-
Diethelm, K.1
Ford, N.J.2
Freed, A.D.3
-
50
-
-
0002795136
-
On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity
-
Keil, F., Mackens, W., Voß, H., Werther, J. (eds.), pp., Springer, Heidelberg
-
Diethelm, K., Freed, A.D.: On the solution of nonlinear fractional differential equations used in the modeling of viscoplasticity. In: Keil, F., Mackens, W., Voß, H., Werther, J. (eds.) Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties, pp. 217–224. Springer, Heidelberg (1999)
-
(1999)
Scientific Computing in Chemical Engineering II: Computational Fluid Dynamics, Reaction Engineering, and Molecular Properties
, pp. 217-224
-
-
Diethelm, K.1
Freed, A.D.2
-
51
-
-
0010186169
-
The FracPECE subroutine for the numerical solution of differential equations of fractional order
-
Heinzel, S., Plesser, T. (eds.), pp., Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen
-
Diethelm, K., Freed, A.D.: The FracPECE subroutine for the numerical solution of differential equations of fractional order. In: Heinzel, S., Plesser, T. (eds.) Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998, pp. 57–71. Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen (1999)
-
(1999)
Forschung Und Wissenschaftliches Rechnen: Beiträge Zum Heinz-Billing-Preis 1998
, pp. 57-71
-
-
Diethelm, K.1
Freed, A.D.2
-
52
-
-
33748663764
-
Numerical solution of linear multi-term initial value problems of fractional order
-
Diethelm, K., Luchko, Y.: Numerical solution of linear multi-term initial value problems of fractional order. J. Comput. Anal. Appl. 6, 243–263 (2004)
-
(2004)
J. Comput. Anal. Appl.
, vol.6
, pp. 243-263
-
-
Diethelm, K.1
Luchko, Y.2
-
53
-
-
0043044718
-
Numerical solution of fractional order differential equations by extrapolation
-
Diethelm, K., Walz, G.: Numerical solution of fractional order differential equations by extrapolation. Numer. Algorithms 16, 231–253 (1997)
-
(1997)
Numer. Algorithms
, vol.16
, pp. 231-253
-
-
Diethelm, K.1
Walz, G.2
-
54
-
-
64549102866
-
A numerical approach for Joulin’s model of a point source initiated flame
-
Diethelm, K., Weilbeer, M.: A numerical approach for Joulin’s model of a point source initiated flame. Fract. Calc. Appl. Anal. 7, 191–212 (2004)
-
(2004)
Fract. Calc. Appl. Anal.
, vol.7
, pp. 191-212
-
-
Diethelm, K.1
Weilbeer, M.2
-
55
-
-
24944498872
-
Weakly singular discrete Gronwall inequalities
-
Dixon, J., McKee, S.: Weakly singular discrete Gronwall inequalities. Z. Angew. Math. Mech. 66, 535–544 (1986)
-
(1986)
Z. Angew. Math. Mech.
, vol.66
, pp. 535-544
-
-
Dixon, J.1
McKee, S.2
-
56
-
-
85072819567
-
Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, 6th edn
-
Doetsch, G.: Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, 6th edn. Oldenbourg, München (1989)
-
(1989)
Oldenbourg, München
-
-
Doetsch, G.1
-
57
-
-
77953539097
-
A commentary on fractionalization of multi-compartmental models
-
Dokoumetzidis, A., Magin, R., Macheras, P.: A commentary on fractionalization of multi-compartmental models. J. Pharmacokinet. Pharmacodyn. 37, 203–207 (2010)
-
(2010)
J. Pharmacokinet. Pharmacodyn.
, vol.37
, pp. 203-207
-
-
Dokoumetzidis, A.1
Magin, R.2
Macheras, P.3
-
58
-
-
0003031851
-
Fractional derivatives and the Cauchy problem for differential equations of fractional order
-
in Russian
-
Dzherbashyan, M.M., Nersesian, A.B.: Fractional derivatives and the Cauchy problem for differential equations of fractional order. Izv. Akad. Nauk Arm. SSR, Mat. 3, 3–29 (1968) (in Russian)
-
(1968)
Izv. Akad. Nauk Arm. SSR, Mat.
, vol.3
, pp. 3-29
-
-
Dzherbashyan, M.M.1
Nersesian, A.B.2
-
59
-
-
0037113861
-
The numerical solution of linear multi-term fractional differential equations: Systems of equations
-
Edwards, J.T., Ford, N.J., Simpson, A.C.: The numerical solution of linear multi-term fractional differential equations: systems of equations. J. Comput. Appl. Math. 148, 401–418 (2002)
-
(2002)
J. Comput. Appl. Math.
, vol.148
, pp. 401-418
-
-
Edwards, J.T.1
Ford, N.J.2
Simpson, A.C.3
-
60
-
-
0011092359
-
A comparison of Adomian’s decomposition method and Runge–Kutta methods for approximate solution of some predator prey model equations. Numerical Analysis Report 309
-
Edwards, J.T., Roberts, J.A., Ford, N.J.: A comparison of Adomian’s decomposition method and Runge–Kutta methods for approximate solution of some predator prey model equations. Numerical Analysis Report 309, Manchester Centre for Computational Mathematics (1997)
-
(1997)
Manchester Centre for Computational Mathematics
-
-
Edwards, J.T.1
Roberts, J.A.2
Ford, N.J.3
-
61
-
-
21344497166
-
An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals
-
Elliott, D.: An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals. IMA J. Numer. Anal. 13, 445–462 (1993)
-
(1993)
IMA J. Numer. Anal.
, vol.13
, pp. 445-462
-
-
Elliott, D.1
-
62
-
-
0003864328
-
-
Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G. (eds.), vol., McGraw-Hill, New York
-
Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G. (eds.): Higher Transcendental Functions, vol. I. McGraw-Hill, New York (1953)
-
(1953)
Higher Transcendental Functions
, vol.1
-
-
-
63
-
-
85013305936
-
-
(eds.): Higher Transcendental Functions, vol. III. McGraw-Hill, New York
-
Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G. (eds.): Higher Transcendental Functions, vol. III. McGraw-Hill, New York (1955)
-
(1955)
Tricomi, F.G
-
-
Erdelyi, A.1
Magnus, W.2
Oberhettinger, F.3
-
64
-
-
85072827605
-
A critical review of the Adomian method. Tech. Report CUED/F-INFENG/TR. 277
-
Fitzgerald, W.J., Leung, C.M.: A critical review of the Adomian method. Tech. Report CUED/F-INFENG/TR. 277. University of Cambridge (1996)
-
(1996)
University of Cambridge
-
-
Fitzgerald, W.J.1
Leung, C.M.2
-
65
-
-
33646341532
-
Comparison of numerical methods for fractional differential equations
-
Ford, N.J., Connolly, J.A.: Comparison of numerical methods for fractional differential equations. Commun. Pure Appl. Anal. 5, 289–307 (2006)
-
(2006)
Commun. Pure Appl. Anal.
, vol.5
, pp. 289-307
-
-
Ford, N.J.1
Connolly, J.A.2
-
66
-
-
67349259080
-
Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations
-
Ford, N.J., Connolly, J.A.: Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations. J. Comput. Appl. Math. 229, 382–391 (2009)
-
(2009)
J. Comput. Appl. Math.
, vol.229
, pp. 382-391
-
-
Ford, N.J.1
Connolly, J.A.2
-
67
-
-
77954333744
-
The approximate solution of fractional differential equations of order greater than
-
Deville, M., Owens, R. (eds.), IMACS, New Brunswick
-
Ford, N.J., Simpson, A.C.: The approximate solution of fractional differential equations of order greater than 1. In: Deville, M., Owens, R. (eds.) Proceedings of the 16th IMACS World Congress on Scientific Computation, Applied Mathematics, and Simulation, Paper 213-1. IMACS, New Brunswick (2000)
-
(2000)
Proceedings of the 16Th IMACS World Congress on Scientific Computation, Applied Mathematics, and Simulation, Paper 213-1
, pp. 1
-
-
Ford, N.J.1
Simpson, A.C.2
-
68
-
-
33750340240
-
Fractional calculus in biomechanics: A 3D viscoelastic model using regularized fractional-derivative kernels with application to the human calcaneal fat pad
-
Freed, A.D., Diethelm, K.: Fractional calculus in biomechanics: a 3D viscoelastic model using regularized fractional-derivative kernels with application to the human calcaneal fat pad. Biomech. Model. Mechanobiol. 5, 203–215 (2006)
-
(2006)
Biomech. Model. Mechanobiol.
, vol.5
, pp. 203-215
-
-
Freed, A.D.1
Diethelm, K.2
-
69
-
-
10644269006
-
Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus (first annual report)
-
NASA Glenn Research Center, Cleveland
-
Freed, A.D., Diethelm, K., Luchko, Y.: Fractional-order viscoelasticity (FOV): constitutive development using the fractional calculus (first annual report). Technical Memorandum 2002-211914, NASA Glenn Research Center, Cleveland (2002)
-
(2002)
Technical Memorandum
, vol.2002
-
-
Freed, A.D.1
Diethelm, K.2
Luchko, Y.3
-
70
-
-
56949091229
-
Fractional Adams–Moulton methods
-
Galeone, L., Garrappa, R.: Fractional Adams–Moulton methods. Math. Comput. Simul. 79, 1358–1367 (2008)
-
(2008)
Math. Comput. Simul.
, vol.79
, pp. 1358-1367
-
-
Galeone, L.1
Garrappa, R.2
-
71
-
-
44949282247
-
Damping description involving fractional operators
-
Gaul, L., Klein, P., Kempfle, S.: Damping description involving fractional operators. Mech. Syst. Signal Process. 5, 81–88 (1991)
-
(1991)
Mech. Syst. Signal Process.
, vol.5
, pp. 81-88
-
-
Gaul, L.1
Klein, P.2
Kempfle, S.3
-
72
-
-
0003625475
-
-
vol., Academic Press, New York
-
Gel’fand, I.M., Shilov, G.E.: Generalized Functions, vol. 1. Academic Press, New York (1964)
-
(1964)
Generalized Functions
, vol.1
-
-
Gel’Fand, I.M.1
Shilov, G.E.2
-
73
-
-
0000983674
-
On a generalization of the Fourier series
-
in Russian
-
Gel’fond, A.O., Leont’ev, A.F.: On a generalization of the Fourier series. Mat. Sb. (N. S.) 29, 477–500 (1951) (in Russian)
-
(1951)
Mat. Sb. (N. S.)
, vol.29
, pp. 477-500
-
-
Gel’Fond, A.O.1
Leont’Ev, A.F.2
-
74
-
-
17844388644
-
A generalization of linear laws of deformation and its application to the problems of internal friction
-
in Russian
-
Gerasimov, A.N.: A generalization of linear laws of deformation and its application to the problems of internal friction. Prikl. Mat. Mekh. 12, 251–260 (1948) (in Russian)
-
(1948)
Prikl. Mat. Mekh.
, vol.12
, pp. 251-260
-
-
Gerasimov, A.N.1
-
75
-
-
0028878140
-
A fractional calculus approach to self-similar protein dynamics
-
Glöckle, W.G., Nonnenmacher, T.F.: A fractional calculus approach to self-similar protein dynamics. Biophys. J. 68, 46–53 (1995)
-
(1995)
Biophys. J.
, vol.68
, pp. 46-53
-
-
Glöckle, W.G.1
Nonnenmacher, T.F.2
-
76
-
-
0345375537
-
Let us teach this generalization of the final-value theorem
-
Gluskin, E.: Let us teach this generalization of the final-value theorem. Eur. J. Phys. 24, 591–597 (2003)
-
(2003)
Eur. J. Phys.
, vol.24
, pp. 591-597
-
-
Gluskin, E.1
-
77
-
-
0001983732
-
Fractional calculus: Some numerical methods
-
Carpinteri, A., Mainardi, F. (eds.), pp., Springer, Wien
-
Gorenflo, R.: Fractional calculus: some numerical methods. In: Carpinteri, A., Mainardi, F. (eds.) Fractals and Fractional Calculus in Continuum Mechanics, pp. 277–290. Springer, Wien (1997)
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 277-290
-
-
Gorenflo, R.1
-
78
-
-
0032647143
-
Discrete random walk models for symmetric Lévy-Feller diffusion processes
-
Gorenflo, R., De Fabritiis, G., Mainardi, F.: Discrete random walk models for symmetric Lévy-Feller diffusion processes. Physica A 269, 79–89 (1999)
-
(1999)
Physica A
, vol.269
, pp. 79-89
-
-
Gorenflo, R.1
de Fabritiis, G.2
Mainardi, F.3
-
79
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
80
-
-
0009450297
-
Fractional oscillations and Mittag-Leffler functions
-
pp., Kuwait
-
Gorenflo, R., Mainardi, F.: Fractional oscillations and Mittag-Leffler functions. In: Proceedings of the International Workshop on the Recent Advances in Applied Mathematics (RAAM ’96), pp. 193–208. Kuwait University, Department of Mathematics and Computer Science, Kuwait (1996)
-
(1996)
Proceedings of the International Workshop on the Recent Advances in Applied Mathematics (RAAM ’96)
, pp. 193-208
-
-
Gorenflo, R.1
Mainardi, F.2
-
81
-
-
0001983732
-
Fractional calculus: Integral and differential equations of fractional order
-
Carpinteri, A., Mainardi, F. (eds.), pp., Springer, Wien
-
Gorenflo, R., Mainardi, F.: Fractional calculus: integral and differential equations of fractional order. In: Carpinteri, A., Mainardi, F. (eds.) Fractals and Fractional Calculus in Continuum Mechanics, pp. 223–276. Springer, Wien (1997)
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 223-276
-
-
Gorenflo, R.1
Mainardi, F.2
-
82
-
-
0003144812
-
On ultraslow and intermediate processes
-
Rusev, P., Dimovski, I., Kiryakova, V. (eds.), pp., Science Culture Technology, Singapore
-
Gorenflo, R., Rutman, R.: On ultraslow and intermediate processes. In: Rusev, P., Dimovski, I., Kiryakova, V. (eds.) Transform Methods and Special Functions, pp. 61–81. Science Culture Technology, Singapore (1995)
-
(1995)
Transform Methods and Special Functions
, pp. 61-81
-
-
Gorenflo, R.1
Rutman, R.2
-
83
-
-
0141996364
-
Fully discrete random walks for space-time fractional diffusion equations
-
Gorenflo, R., Vivoli, A.: Fully discrete random walks for space-time fractional diffusion equations. Signal Process. 83, 2411–2420 (2003)
-
(2003)
Signal Process
, vol.83
, pp. 2411-2420
-
-
Gorenflo, R.1
Vivoli, A.2
-
84
-
-
36849117395
-
On creep and relaxation
-
Gross, B.: On creep and relaxation. J. Appl. Phys. 18, 212–221 (1947)
-
(1947)
J. Appl. Phys.
, vol.18
, pp. 212-221
-
-
Gross, B.1
-
85
-
-
0000238491
-
Über “begrenzte” Derivationen und deren Anwendung
-
Grünwald, A.K.: Über “begrenzte” Derivationen und deren Anwendung. Z. Angew. Math. Phys. 12, 441–480 (1867)
-
(1867)
Z. Angew. Math. Phys.
, vol.12
, pp. 441-480
-
-
Grünwald, A.K.1
-
86
-
-
85072824494
-
Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale Univ. Press, New Haven (1923); reprinted by Dover
-
Hadamard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale Univ. Press, New Haven (1923); reprinted by Dover, New York (1952)
-
(1952)
New York
-
-
Hadamard, J.1
-
87
-
-
8844268216
-
Some existence theorems on differential equations of generalized order through a fixed-point theorem
-
Hadid, S.B., Ta’ani, A.A., Momani, S.M.: Some existence theorems on differential equations of generalized order through a fixed-point theorem. J. Fract. Calc. 9, 45–49 (1996)
-
(1996)
J. Fract. Calc.
, vol.9
, pp. 45-49
-
-
Hadid, S.B.1
Ta’Ani, A.A.2
Momani, S.M.3
-
88
-
-
0003589989
-
-
2nd edn. Springer, Berlin
-
Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd edn. Springer, Berlin (1993)
-
(1993)
Solving Ordinary Differential Equations I: Nonstiff Problems
-
-
Hairer, E.1
Nørsett, S.P.2
Wanner, G.3
-
91
-
-
0032308350
-
Approximate solution of non linear differential equations with convolution product nonlinearities
-
He, J.H.: Approximate solution of non linear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Eng. 167, 69–73 (1998)
-
(1998)
Comput. Methods Appl. Mech. Eng.
, vol.167
, pp. 69-73
-
-
He, J.H.1
-
92
-
-
34250668369
-
Variational iteration method – some recent results and new interpretations
-
He, J.H.: Variational iteration method – some recent results and new interpretations. J. Comput. Appl. Math. 207, 3–17 (2007)
-
(2007)
J. Comput. Appl. Math.
, vol.207
, pp. 3-17
-
-
He, J.H.1
-
98
-
-
0035995563
-
The curious history of Faà di Bruno’s formula
-
Johnson, W.P.: The curious history of Faà di Bruno’s formula. Am. Math. Mon. 109, 217–234 (2002)
-
(2002)
Am. Math. Mon.
, vol.109
, pp. 217-234
-
-
Johnson, W.P.1
-
99
-
-
84950202291
-
Point-source initiation of lean spherical flames of light reactants: An asymptotic theory
-
Joulin, G.: Point-source initiation of lean spherical flames of light reactants: an asymptotic theory. Combust. Sci. Technol. 43, 99–113 (1985)
-
(1985)
Combust. Sci. Technol.
, vol.43
, pp. 99-113
-
-
Joulin, G.1
-
100
-
-
33847309315
-
-
Elsevier, Amsterdam
-
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
-
(2006)
Theory and Applications of Fractional Differential Equations
-
-
Kilbas, A.A.1
Srivastava, H.M.2
Trujillo, J.J.3
-
101
-
-
1242327688
-
Differential equations of fractional order. Methods, results and problems
-
Kilbas, A.A., Trujillo, J.J.: Differential equations of fractional order. Methods, results and problems. I. Appl. Anal. 78, 153–192 (2001)
-
(2001)
I. Appl. Anal.
, vol.78
, pp. 153-192
-
-
Kilbas, A.A.1
Trujillo, J.J.2
-
102
-
-
25144514177
-
Differential equations of fractional order. Methods, results and problems. II
-
Kilbas, A.A., Trujillo, J.J.: Differential equations of fractional order. Methods, results and problems. II. Appl. Anal. 81, 435–493 (2002)
-
(2002)
Appl. Anal.
, vol.81
, pp. 435-493
-
-
Kilbas, A.A.1
Trujillo, J.J.2
-
103
-
-
76449114769
-
The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus
-
Kiryakova, V.: The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus. Comput. Math. Appl. 59, 1885–1895 (2010)
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1885-1895
-
-
Kiryakova, V.1
-
104
-
-
74149091657
-
The special functions of fractional calculus as generalized fractional calculus operators of some basic functions
-
Kiryakova, V.: The special functions of fractional calculus as generalized fractional calculus operators of some basic functions. Comput. Math. Appl. 59, 1128–1141 (2010)
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1128-1141
-
-
Kiryakova, V.1
-
105
-
-
84889299911
-
-
Klages, R., Radons, G., Sokolov, I.M. (eds.), Wiley-VCH, Weinheim
-
Klages, R., Radons, G., Sokolov, I.M. (eds.): Anomalous Transport: Foundations and Applications. Wiley-VCH, Weinheim (2008)
-
(2008)
Anomalous Transport: Foundations and Applications
-
-
-
106
-
-
77956168580
-
Fractional differential equations: α-entire solutions, regular and irregular singularities
-
Kochubei, A.N.: Fractional differential equations: α-entire solutions, regular and irregular singularities. Fract. Calc. Appl. Anal. 12, 135–158 (2009)
-
(2009)
Fract. Calc. Appl. Anal.
, vol.12
, pp. 135-158
-
-
Kochubei, A.N.1
-
107
-
-
0022700808
-
Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics
-
Koeller, R.C.: Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics. Acta Mech. 58, 251–264 (1986)
-
(1986)
Acta Mech
, vol.58
, pp. 251-264
-
-
Koeller, R.C.1
-
110
-
-
0038053920
-
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
-
Lederman, C., Roquejoffre, J.-M., Wolanski, N.: Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames. C. R. Math. Acad. Sci. Paris 334, 569–574 (2002)
-
(2002)
C. R. Math. Acad. Sci. Paris
, vol.334
, pp. 569-574
-
-
Lederman, C.1
Roquejoffre, J.-M.2
Wolanski, N.3
-
111
-
-
34548052741
-
-
Mehauté, A., Tenreiro Machado, J.A., Trigeassou, J.C., Sabatier, J. (eds.), Ubooks, Neusäß
-
Le Mehauté, A., Tenreiro Machado, J.A., Trigeassou, J.C., Sabatier, J. (eds.): Fractional Differentiation and Its Applications. Ubooks, Neusäß (2005)
-
(2005)
Fractional Differentiation and Its Applications
-
-
-
112
-
-
0001936243
-
Theory of differentiation with an arbitrary index
-
in Russian
-
Letnikov, A.V.: Theory of differentiation with an arbitrary index. Mat. Sb. 3, 1–66 (1868) (in Russian)
-
(1868)
Mat. Sb.
, vol.3
, pp. 1-66
-
-
Letnikov, A.V.1
-
113
-
-
67349162538
-
Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation
-
Liang, S., Jeffrey, D.J.: Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Commun. Nonlinear Sci. Numer. Simulat. 14, 4057–4064 (2009)
-
(2009)
Commun. Nonlinear Sci. Numer. Simulat.
, vol.14
, pp. 4057-4064
-
-
Liang, S.1
Jeffrey, D.J.2
-
116
-
-
0002588201
-
Memoire sur quelques questions de géometrie et de mécanique, et sur un nouveau gentre pour resoudre ces questions
-
Liouville J.: Memoire sur quelques questions de géometrie et de mécanique, et sur un nouveau gentre pour resoudre ces questions. J. Ecole Polytech. 13, 1–69 (1832)
-
(1832)
J. Ecole Polytech.
, vol.13
, pp. 1-69
-
-
Liouville, J.1
-
117
-
-
0003707239
-
-
2nd edn. Chelsea Publ. Comp., New York
-
Lorentz, G.G.: Bernstein Polynomials, 2nd edn. Chelsea Publ. Comp., New York (1986)
-
(1986)
Bernstein Polynomials
-
-
Lorentz, G.G.1
-
118
-
-
19744367302
-
Wave field simulation for heterogeneous porous media with singular memory drag force
-
Lu, J.-F., Hanyga, A.: Wave field simulation for heterogeneous porous media with singular memory drag force. J. Comput. Phys. 208, 651–674 (2005)
-
(2005)
J. Comput. Phys.
, vol.208
, pp. 651-674
-
-
Lu, J.-F.1
Hanyga, A.2
-
119
-
-
33646366905
-
Chaotic dynamics of the fractional-order Lü system and its synchronization
-
Lu, J.G.: Chaotic dynamics of the fractional-order Lü system and its synchronization. Phys. Lett. A 354, 305–311 (2006)
-
(2006)
Phys. Lett. A
, vol.354
, pp. 305-311
-
-
Lu, J.G.1
-
120
-
-
84962571892
-
Runge-Kutta theory for Volterra and Abel integral equations of the second kind
-
Lubich, C.: Runge-Kutta theory for Volterra and Abel integral equations of the second kind. Math. Comput. 41, 87–102 (1983)
-
(1983)
Math. Comput.
, vol.41
, pp. 87-102
-
-
Lubich, C.1
-
121
-
-
0000717432
-
Discretized fractional calculus
-
Lubich, C.: Discretized fractional calculus. SIAM J. Math. Anal. 17, 704–719 (1986)
-
(1986)
SIAM J. Math. Anal.
, vol.17
, pp. 704-719
-
-
Lubich, C.1
-
122
-
-
77952646760
-
A survey of weighted polynomial approximation with exponential weights
-
Lubinsky, D.S.: A survey of weighted polynomial approximation with exponential weights. Surv. Approx. Theory 3, 1–105 (2007)
-
(2007)
Surv. Approx. Theory
, vol.3
, pp. 1-105
-
-
Lubinsky, D.S.1
-
123
-
-
0012659515
-
An operational method for solving fractional differential equations with the Caputo derivatives
-
Luchko, Y., Gorenflo, R.: An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math. Vietnamica 24, 207–233 (1999)
-
(1999)
Acta Math. Vietnamica
, vol.24
, pp. 207-233
-
-
Luchko, Y.1
Gorenflo, R.2
-
125
-
-
0001983732
-
Fractional calculus: Some basic problems in continuum and statistical mechanics
-
Carpinteri, A., Mainardi, F. (eds.), pp., Springer, Wien
-
Mainardi, F.: Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri, A., Mainardi, F. (eds.) Fractals and Fractional Calculus in Continuum Mechanics, pp. 291–348. Springer, Wien (1997)
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
-
127
-
-
0000145521
-
On Mittag-Leffler-type functions in fractional evolution processes
-
Mainardi, F., Gorenflo, R.: On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math. 118, 283–299 (2000)
-
(2000)
J. Comput. Appl. Math.
, vol.118
, pp. 283-299
-
-
Mainardi, F.1
Gorenflo, R.2
-
128
-
-
0034502929
-
Fractional calculus and continuous-time finance II: The waiting-time distribution
-
Mainardi, F., Raberto, M., Gorenflo, R., Scalas, E.: Fractional calculus and continuous-time finance II: the waiting-time distribution. Physica A 287, 468–481 (2000)
-
(2000)
Physica A
, vol.287
, pp. 468-481
-
-
Mainardi, F.1
Raberto, M.2
Gorenflo, R.3
Scalas, E.4
-
129
-
-
0000631760
-
Sur les dérivées et sur les différences des fonctions de variables réelles
-
Marchaud, A.: Sur les dérivées et sur les différences des fonctions de variables réelles. J. Math. 6, 337–425 (1927)
-
(1927)
J. Math.
, vol.6
, pp. 337-425
-
-
Marchaud, A.1
-
130
-
-
0019606817
-
Differintegral interpolation from a bandlimited signal’s samples
-
Marks, R.J. II, Hall, M.W.: Differintegral interpolation from a bandlimited signal’s samples. IEEE Trans. Acoust. Speech Signal Process. 29, 872–877 (1981)
-
(1981)
IEEE Trans. Acoust. Speech Signal Process.
, vol.29
, pp. 872-877
-
-
Marks, R.J.1
Hall, M.W.2
-
133
-
-
85072833819
-
-
(eds.): Fractional Differential Systems: Models, Methods, and Applications. SMAI, Paris
-
Matignon, D., Montseny, G. (eds.): Fractional Differential Systems: Models, Methods, and Applications. SMAI, Paris (1998)
-
(1998)
Montseny, G
-
-
Matignon, D.1
-
134
-
-
0001044887
-
Relaxation in filled polymers: A fractional calculus approach
-
Metzler, R., Schick, W., Kilian, H.-G., Nonnenmacher, T.F.: Relaxation in filled polymers: a fractional calculus approach. J. Chem. Phys. 103, 7180–7186 (1995)
-
(1995)
J. Chem. Phys.
, vol.103
, pp. 7180-7186
-
-
Metzler, R.1
Schick, W.2
Kilian, H.-G.3
Nonnenmacher, T.F.4
-
136
-
-
33746839018
-
Une généralisation de l’intégrale de Laplace-Abel
-
Mittag-Leffler, G.M.: Une généralisation de l’intégrale de Laplace-Abel. C. R. Acad. Sci. Paris (Ser. II) 136, 537–539 (1903)
-
(1903)
C. R. Acad. Sci. Paris (Ser. II)
, vol.136
, pp. 537-539
-
-
Mittag-Leffler, G.M.1
-
138
-
-
8844274113
-
Local and global uniqueness theorems on differential equations of noninteger order via Bihari’s and Gronwall’s inequalities
-
Momani, S.M.: Local and global uniqueness theorems on differential equations of noninteger order via Bihari’s and Gronwall’s inequalities. Rev. Téc. Fac. Ing. Univ. Zulia 23, 66–69 (2000)
-
(2000)
Rev. Téc. Fac. Ing. Univ. Zulia
, vol.23
, pp. 66-69
-
-
Momani, S.M.1
-
139
-
-
34247395044
-
Homotopy perturbation method for nonlinear partial differential equations of fractional order
-
Momani, S., Odibat, Z.: Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 365, 345–350 (2007)
-
(2007)
Phys. Lett. A
, vol.365
, pp. 345-350
-
-
Momani, S.1
Odibat, Z.2
-
141
-
-
21344465606
-
On the Riemann–Liouville fractional calculus and some recent applications
-
Nonnenmacher, T.F., Metzler, R.: On the Riemann–Liouville fractional calculus and some recent applications. Fractals 3, 557–566 (1995)
-
(1995)
Fractals
, vol.3
, pp. 557-566
-
-
Nonnenmacher, T.F.1
Metzler, R.2
-
142
-
-
0000266650
-
A new general law of deformation
-
Nutting, P.G.: A new general law of deformation. J. Franklin Inst. 191, 679–685 (1921)
-
(1921)
J. Franklin Inst.
, vol.191
, pp. 679-685
-
-
Nutting, P.G.1
-
143
-
-
0343020693
-
A general stress–strain–time formula
-
Nutting, P.G.: A general stress–strain–time formula. J. Franklin Inst. 235, 513–524 (1943)
-
(1943)
J. Franklin Inst.
, vol.235
, pp. 513-524
-
-
Nutting, P.G.1
-
144
-
-
74149090385
-
Analytic study on linear systems of fractional differential equations
-
Odibat, Z.M.: Analytic study on linear systems of fractional differential equations. Comput. Math. Appl. 59, 1171–1183 (2010)
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1171-1183
-
-
Odibat, Z.M.1
-
145
-
-
39449122795
-
Generalized differential transform method: Application to differential equations of fractional order
-
Odibat, Z., Momani, S., Erturk, V.S.: Generalized differential transform method: application to differential equations of fractional order. Appl. Math. Comput. 197, 467–477 (2008)
-
(2008)
Appl. Math. Comput.
, vol.197
, pp. 467-477
-
-
Odibat, Z.1
Momani, S.2
Erturk, V.S.3
-
147
-
-
0016941699
-
Diffusion in a semi-infinite region with nonlinear surface dissipation
-
Olmstead, W.E., Handelsman, R.A.: Diffusion in a semi-infinite region with nonlinear surface dissipation. SIAM Rev. 18, 275–291 (1976)
-
(1976)
SIAM Rev
, vol.18
, pp. 275-291
-
-
Olmstead, W.E.1
Handelsman, R.A.2
-
148
-
-
77956143817
-
Über Integration von gewöhnlichen Differentialgleichungen durch Reihen. Sitz.-Ber. Heidelberger Akademie der Wissenschaften A Math.-Nat
-
Perron, O.: Über Integration von gewöhnlichen Differentialgleichungen durch Reihen. Sitz.-Ber. Heidelberger Akademie der Wissenschaften A Math.-Nat. Klasse Abhandlung 2 (1919)
-
(1919)
Klasse Abhandlung
, pp. 2
-
-
Perron, O.1
-
152
-
-
0003767029
-
Fractional-order systems and fractional-order controllers. Technical report UEF-03-94, Institute for Experimental Physics, Slovak
-
Podlubny, I.: Fractional-order systems and fractional-order controllers. Technical report UEF-03-94, Institute for Experimental Physics, Slovak Acad. Sci. (1994)
-
(1994)
Acad. Sci.
-
-
Podlubny, I.1
-
154
-
-
0242354999
-
Geometric and physical interpretation of fractional integration and fractional differentiation
-
Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5, 367–386 (2002)
-
(2002)
Fract. Calc. Appl. Anal.
, vol.5
, pp. 367-386
-
-
Podlubny, I.1
-
155
-
-
0000169312
-
Application of fractional-order derivatives to calculation of heat load intensity change in blast furnace walls
-
Podlubny, I., Dorcak, L., Misanek, J.: Application of fractional-order derivatives to calculation of heat load intensity change in blast furnace walls. Trans. Tech. Univ. Košice 5, 137–144 (1995)
-
(1995)
Trans. Tech. Univ. Košice
, vol.5
, pp. 137-144
-
-
Podlubny, I.1
Dorcak, L.2
Misanek, J.3
-
156
-
-
77953539358
-
A new approach to the compartmental analysis in pharmacokinetics: Fractional time evolution of Diclofenac
-
Popović, J.K., Atanacković, M.T., Pilipović, A.S., Rapaić, M.R., Pilipović, S., Atanacković, T.M.: A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of Diclofenac. J. Pharmacokinet. Pharmacodyn. 37, 119–134 (2010)
-
(2010)
J. Pharmacokinet. Pharmacodyn.
, vol.37
, pp. 119-134
-
-
Popović, J.K.1
Atanacković, M.T.2
Pilipović, A.S.3
Rapaić, M.R.4
Pilipović, S.5
Atanacković, T.M.6
-
157
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
158
-
-
50549176610
-
The initial-and final-value theorems in Laplace transform theory
-
Rasof, B.: The initial-and final-value theorems in Laplace transform theory. J. Franklin Inst. 274, 165–177 (1962)
-
(1962)
J. Franklin Inst.
, vol.274
, pp. 165-177
-
-
Rasof, B.1
-
159
-
-
0002588102
-
Nonlinear dynamical systems: On the accuracy of Adomian’s decomposition method
-
Répaci, A.: Nonlinear dynamical systems: on the accuracy of Adomian’s decomposition method. Appl. Math. Lett. 3(4), 35–39 (1990)
-
(1990)
Appl. Math. Lett.
, vol.3
, Issue.4
, pp. 35-39
-
-
Répaci, A.1
-
160
-
-
84941377590
-
Auflösung einer mechanischen Aufgabe
-
Abel, N.H.: Auflösung einer mechanischen Aufgabe. J. Reine Angew. Math. 1, 153–157 (1826)
-
(1826)
J. Reine Angew. Math.
, Issue.1
, pp. 153-157
-
-
Abel, N.H.1
-
161
-
-
0042762748
-
Ignition and propagation in an integro-differential model for spherical flames
-
Roquejoffre, J.-M., Vázquez, J.-L.: Ignition and propagation in an integro-differential model for spherical flames. Discrete Contin. Dyn. Syst. Ser. B 2, 379–387 (2002)
-
(2002)
Discrete Contin. Dyn. Syst. Ser. B
, vol.2
, pp. 379-387
-
-
Roquejoffre, J.-M.1
Vázquez, J.-L.2
-
162
-
-
23644455602
-
The development of fractional calculus 1695–1900
-
Ross, B.: The development of fractional calculus 1695–1900. Hist. Math. 4, 75–89 (1977)
-
(1977)
Hist. Math.
, vol.4
, pp. 75-89
-
-
Ross, B.1
-
163
-
-
77955238264
-
Reflections on two parallel ways in the progress of fractional calculus in mechanics of solids
-
Rossikhin, Yu.A.: Reflections on two parallel ways in the progress of fractional calculus in mechanics of solids. Appl. Mech. Rev. 63, 010701 (2010)
-
(2010)
Appl. Mech. Rev.
, vol.63
-
-
Rossikhin, Y.A.1
-
164
-
-
77954346342
-
Comparative analysis of viscoelastic models involving fractional derivatives of different orders
-
Rossikhin, Yu.A., Shitikova, M.V.: Comparative analysis of viscoelastic models involving fractional derivatives of different orders. Fract. Calc. Appl. Anal. 10, 111–121 (2007)
-
(2007)
Fract. Calc. Appl. Anal.
, vol.10
, pp. 111-121
-
-
Rossikhin, Y.A.1
Shitikova, M.V.2
-
166
-
-
84885710343
-
-
Sabatier, J., Agrawal, O.P., Tenreiro Machado, J.A. (eds.), Springer, Dordrecht
-
Sabatier, J., Agrawal, O.P., Tenreiro Machado, J.A. (eds.): Advances in Fractional Calculus. Springer, Dordrecht (2007)
-
(2007)
Advances in Fractional Calculus
-
-
-
168
-
-
0041014183
-
Integral representation of remainders
-
Sard, A.: Integral representation of remainders. Duke Math. J. 15, 333–345 (1948)
-
(1948)
Duke Math. J.
, vol.15
, pp. 333-345
-
-
Sard, A.1
-
169
-
-
0034275979
-
Fractional calculus and continuous-time finance
-
Scalas, E., Gorenflo, R., Mainardi, F.: Fractional calculus and continuous-time finance. Physica A 284, 376–384 (2000)
-
(2000)
Physica A
, vol.284
, pp. 376-384
-
-
Scalas, E.1
Gorenflo, R.2
Mainardi, F.3
-
170
-
-
1842531858
-
Uncoupled continuous-time random walks: Analytic solution and limiting behaviour of the master equation
-
Scalas, E., Gorenflo, R., Mainardi, F.: Uncoupled continuous-time random walks: analytic solution and limiting behaviour of the master equation. Phys. Rev. E 69, 011107 (2004)
-
(2004)
Phys. Rev. E
, vol.69
-
-
Scalas, E.1
Gorenflo, R.2
Mainardi, F.3
-
171
-
-
26444463136
-
On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems
-
Schmidt, A., Gaul, L.: On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems. Mech. Res. Commun. 33, 99–107 (2006)
-
(2006)
Mech. Res. Commun.
, vol.33
, pp. 99-107
-
-
Schmidt, A.1
Gaul, L.2
-
172
-
-
0006981852
-
The rheological law underlying the Nutting equation
-
Scott Blair, G.W., Reiner, M.: The rheological law underlying the Nutting equation. Appl. Sci. Res. 2, 225–234 (1951)
-
(1951)
Appl. Sci. Res.
, vol.2
, pp. 225-234
-
-
Scott Blair, G.W.1
Reiner, M.2
-
173
-
-
34249763957
-
Asymptotic formulae for zeros of a function of Mittag-Leffler’s type
-
in Russian
-
Sedletskij, A.M.: Asymptotic formulae for zeros of a function of Mittag-Leffler’s type. Anal. Math. 20, 117–132 (1994) (in Russian)
-
(1994)
Anal. Math.
, vol.20
, pp. 117-132
-
-
Sedletskij, A.M.1
-
174
-
-
55349118252
-
Numerical results for the generalized Mittag-Leffler functions
-
Seybold, H.J., Hilfer, R.: Numerical results for the generalized Mittag-Leffler functions. Fract. Calc. Appl. Anal. 8, 127–139 (2005)
-
(2005)
Fract. Calc. Appl. Anal.
, vol.8
, pp. 127-139
-
-
Seybold, H.J.1
Hilfer, R.2
-
175
-
-
55349106156
-
Numerical algorithm for calculating the generalized Mittag-Leffler function
-
Seybold, H.J., Hilfer, R.: Numerical algorithm for calculating the generalized Mittag-Leffler function. SIAM J. Numer. Anal. 47, 69–88 (2008)
-
(2008)
SIAM J. Numer. Anal.
, vol.47
, pp. 69-88
-
-
Seybold, H.J.1
Hilfer, R.2
-
177
-
-
33745906525
-
Galerkin projections and finite elements for fractional order derivatives
-
Singh, S.J., Chatterjee, A.: Galerkin projections and finite elements for fractional order derivatives. Nonlinear Dynam. 45, 183–206 (2006)
-
(2006)
Nonlinear Dynam
, vol.45
, pp. 183-206
-
-
Singh, S.J.1
Chatterjee, A.2
-
178
-
-
70349789880
-
Dynamical models of happiness with fractional order
-
Song, L., Xu, S.Y., Yang, J.Y.: Dynamical models of happiness with fractional order. Commun. Nonlinear Sci. Numer. Simulat. 15, 616–628 (2010)
-
(2010)
Commun. Nonlinear Sci. Numer. Simulat.
, vol.15
, pp. 616-628
-
-
Song, L.1
Xu, S.Y.2
Yang, J.Y.3
-
180
-
-
58149510910
-
-
Taş, K., Tenreiro Machado, J.A., Baleanu, D. (eds.), Springer, Dordrecht
-
Taş, K., Tenreiro Machado, J.A., Baleanu, D. (eds.): Mathematical Methods in Engineering. Springer, Dordrecht (2007)
-
(2007)
Mathematical Methods in Engineering
-
-
-
181
-
-
34250696383
-
On the convergence of He’s variational iteration method
-
Tatari, M., Dehghan, M.: On the convergence of He’s variational iteration method. J. Comput. Appl. Math. 207, 121–128 (2007)
-
(2007)
J. Comput. Appl. Math.
, vol.207
, pp. 121-128
-
-
Tatari, M.1
Dehghan, M.2
-
182
-
-
67650122083
-
Comments on stability analysis of a class of nonlinear fractional-order systems
-
Tavazoei, M.S.: Comments on stability analysis of a class of nonlinear fractional-order systems. IEEE Trans. Circ. Syst. II 56, 519–520 (2009)
-
(2009)
IEEE Trans. Circ. Syst. II
, vol.56
, pp. 519-520
-
-
Tavazoei, M.S.1
-
183
-
-
67649624652
-
Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems
-
Tavazoei, M.S., Haeri, M., Bolouki, S., Siami, M.: Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems. SIAM J. Numer. Anal. 47, 321–328 (2008)
-
(2008)
SIAM J. Numer. Anal.
, vol.47
, pp. 321-328
-
-
Tavazoei, M.S.1
Haeri, M.2
Bolouki, S.3
Siami, M.4
-
184
-
-
0021439912
-
On the appearance of the fractional derivative in the behavior of real materials
-
Torvik, P.J., Bagley, R.L.: On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. 51, 294–298 (1984)
-
(1984)
J. Appl. Mech.
, vol.51
, pp. 294-298
-
-
Torvik, P.J.1
Bagley, R.L.2
-
185
-
-
0036869926
-
Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals
-
Trinks, C., Ruge, P.: Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals. Comput. Mech. 29, 471–476 (2002)
-
(2002)
Comput. Mech.
, vol.29
, pp. 471-476
-
-
Trinks, C.1
Ruge, P.2
-
186
-
-
70749123687
-
Method of Fractional Derivatives
-
Artishok Publ. House, in Russian
-
Uchaikin, V.V.: Method of Fractional Derivatives. Artishok Publ. House, Ul’yanovsk (2008) (in Russian)
-
(2008)
Ul’yanovsk
-
-
Uchaikin, V.V.1
-
187
-
-
77953541437
-
Fractional compartmental models and multi-term Mittag-Leffler response functions
-
Verotta, D.: Fractional compartmental models and multi-term Mittag-Leffler response functions. J. Pharmacokinet. Pharmacodyn. 37, 209–215 (2010)
-
(2010)
J. Pharmacokinet. Pharmacodyn.
, vol.37
, pp. 209-215
-
-
Verotta, D.1
-
189
-
-
84979309618
-
Zur Theorie und Anwendung des Iterationsverfahrens
-
Weissinger, J.: Zur Theorie und Anwendung des Iterationsverfahrens. Math. Nachr. 8, 193–212 (1952)
-
(1952)
Math. Nachr.
, vol.8
, pp. 193-212
-
-
Weissinger, J.1
-
191
-
-
0001799540
-
α(x)
-
α(x). Acta Math. 29, 191–201 (1905)
-
(1905)
Acta Math
, vol.29
, pp. 191-201
-
-
Wiman, A.1
-
192
-
-
0039293970
-
α(x)
-
α(x). Acta Math. 29, 217–234 (1905)
-
(1905)
Acta Math
, vol.29
, pp. 217-234
-
-
Wiman, A.1
-
193
-
-
0033433331
-
Analytic continuation of operators. Applications: From number theory and group theory to quantum field and string theories
-
Woon, S.C.: Analytic continuation of operators. Applications: from number theory and group theory to quantum field and string theories. Rev. Math. Phys. 11, 463–501 (1999)
-
(1999)
Rev. Math. Phys.
, vol.11
, pp. 463-501
-
-
Woon, S.C.1
-
194
-
-
0036554885
-
A numerical scheme for dynamic systems containing fractional derivatives
-
Yuan, L., Agrawal, O.P.: A numerical scheme for dynamic systems containing fractional derivatives. J. Vib. Acoust. 124, 321–324 (2002)
-
(2002)
J. Vib. Acoust.
, vol.124
, pp. 321-324
-
-
Yuan, L.1
Agrawal, O.P.2
|