-
1
-
-
0022660581
-
On the fractional calculus models of viscoelastic behaviour
-
Bagley R.L., and Torvik P.L. On the fractional calculus models of viscoelastic behaviour. J. Rheol. 30 (1986) 133-155
-
(1986)
J. Rheol.
, vol.30
, pp. 133-155
-
-
Bagley, R.L.1
Torvik, P.L.2
-
5
-
-
0001869174
-
On the initial value problem for the fractional diffusion-wave equation
-
Rionero S., and Ruggeri T. (Eds), World Scientific Publishing Company, Singapore
-
Mainardi F. On the initial value problem for the fractional diffusion-wave equation. In: Rionero S., and Ruggeri T. (Eds). Waves and Stability in Continuous Media (Bologna 1993) (1994), World Scientific Publishing Company, Singapore 246-251
-
(1994)
Waves and Stability in Continuous Media (Bologna 1993)
, pp. 246-251
-
-
Mainardi, F.1
-
7
-
-
0030867045
-
Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids
-
Rossikhin Y., and Shitikova M. Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids. Appl. Mech. Rev. 50 (1997) 15-67
-
(1997)
Appl. Mech. Rev.
, vol.50
, pp. 15-67
-
-
Rossikhin, Y.1
Shitikova, M.2
-
8
-
-
0001983732
-
Fractional calculus: Some basic problems in continuum and statistical mechanics
-
Carpinteri A., and Mainardi F. (Eds), Springer-Verlag, Wien
-
Mainardi F. Fractional calculus: Some basic problems in continuum and statistical mechanics. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer-Verlag, Wien 291-348
-
(1997)
Fractals and Fractional Calculus in Continuum Mechanics
, pp. 291-348
-
-
Mainardi, F.1
-
10
-
-
0002641421
-
The random walks guide to anomalous diffusion: A fractional dynamic approach
-
Metzler R., and Klafter J. The random walks guide to anomalous diffusion: A fractional dynamic approach. Phys. Rep. 339 1 (2000) 1-77
-
(2000)
Phys. Rep.
, vol.339
, Issue.1
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
11
-
-
0003427295
-
-
Hilfer R. (Ed), World Scientific Publishing Company, Singapore, London
-
In: Hilfer R. (Ed). Applications of Fractional Calculus in Physics (2000), World Scientific Publishing Company, Singapore, London
-
(2000)
Applications of Fractional Calculus in Physics
-
-
-
12
-
-
0242458154
-
A chaos neuron model with fractional differential equation
-
Matsuzaki T., and Nakagawa M. A chaos neuron model with fractional differential equation. J. Phys. Soc. Japan. 72 (2003) 2678-2684
-
(2003)
J. Phys. Soc. Japan.
, vol.72
, pp. 2678-2684
-
-
Matsuzaki, T.1
Nakagawa, M.2
-
13
-
-
3042776917
-
Fractional calculus in bioengineering
-
Magin R.L. Fractional calculus in bioengineering. Crit. Rev. Biomed. Eng. 32 (2004) 1-104
-
(2004)
Crit. Rev. Biomed. Eng.
, vol.32
, pp. 1-104
-
-
Magin, R.L.1
-
16
-
-
34247323827
-
Fractional differential equations as alternative models to nonlinear differential equations
-
Bonilla B., Rivero M., Rodríguez-Germá L., and Trujillo J.J. Fractional differential equations as alternative models to nonlinear differential equations. Appl. Math. Comput. 187 1 (2007) 79-88
-
(2007)
Appl. Math. Comput.
, vol.187
, Issue.1
, pp. 79-88
-
-
Bonilla, B.1
Rivero, M.2
Rodríguez-Germá, L.3
Trujillo, J.J.4
-
18
-
-
0001553919
-
Fractional diffusion and wave equations
-
Schneider W., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989) 134-144
-
(1989)
J. Math. Phys.
, vol.30
, pp. 134-144
-
-
Schneider, W.1
Wyss, W.2
-
19
-
-
0001407424
-
The fundamental solution of the space-time fractional diffusion equation
-
Mainardi F., Luchko Y., and Pagnini G. The fundamental solution of the space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 4 (2001) 153-192
-
(2001)
Fract. Calc. Appl. Anal.
, vol.4
, pp. 153-192
-
-
Mainardi, F.1
Luchko, Y.2
Pagnini, G.3
-
20
-
-
0036650479
-
A predictor-corrector approach for the numerical solution of fractional differential equations
-
Diethelm K., Ford N., and Freed A. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam. 29 (2002) 3-22
-
(2002)
Nonlinear Dynam.
, vol.29
, pp. 3-22
-
-
Diethelm, K.1
Ford, N.2
Freed, A.3
-
21
-
-
4043121080
-
Detailed error analysis for a fractional Adams Method
-
Diethelm K., Ford N., and Freed A. Detailed error analysis for a fractional Adams Method. Numer. Algorithms 36 (2004) 31-52
-
(2004)
Numer. Algorithms
, vol.36
, pp. 31-52
-
-
Diethelm, K.1
Ford, N.2
Freed, A.3
-
22
-
-
74149085984
-
An algorithm for the numerical solution of differential equations of fractional order
-
Odibat Z., and Momani S. An algorithm for the numerical solution of differential equations of fractional order. J. Appl. Math. Inform. 26 1-2 (2008) 15-27
-
(2008)
J. Appl. Math. Inform.
, vol.26
, Issue.1-2
, pp. 15-27
-
-
Odibat, Z.1
Momani, S.2
-
23
-
-
34548384362
-
Numerical methods for nonlinear partial differential equations of fractional order
-
Odibat Z., and Momani S. Numerical methods for nonlinear partial differential equations of fractional order. Appl. Math. Modelling. 32 12 (2008) 28-39
-
(2008)
Appl. Math. Modelling.
, vol.32
, Issue.12
, pp. 28-39
-
-
Odibat, Z.1
Momani, S.2
-
24
-
-
35348869861
-
Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order
-
Odibat Z., and Momani S. Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order. Chaos Solitons Fractals 36 1 (2008) 167-174
-
(2008)
Chaos Solitons Fractals
, vol.36
, Issue.1
, pp. 167-174
-
-
Odibat, Z.1
Momani, S.2
-
25
-
-
64549148828
-
Series solutions of non-linear Riccati differential equations with fractional order
-
Cang J., Tan Y., Xu H., and Liao S.J. Series solutions of non-linear Riccati differential equations with fractional order. Chaos Solitons Fractals 40 1 (2009) 1-9
-
(2009)
Chaos Solitons Fractals
, vol.40
, Issue.1
, pp. 1-9
-
-
Cang, J.1
Tan, Y.2
Xu, H.3
Liao, S.J.4
-
26
-
-
47849126401
-
A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
-
Momani S., and Odibat Z. A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula. J. Comput. Appl. Math. 220 1-2 (2008) 85-95
-
(2008)
J. Comput. Appl. Math.
, vol.220
, Issue.1-2
, pp. 85-95
-
-
Momani, S.1
Odibat, Z.2
-
27
-
-
30344464250
-
Application of variational iteration method to nonlinear differential equations of fractional order
-
Odibat Z., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul. 7 1 (2006) 27-34
-
(2006)
Int. J. Nonlinear Sci. Numer. Simul.
, vol.7
, Issue.1
, pp. 27-34
-
-
Odibat, Z.1
Momani, S.2
-
28
-
-
0030528474
-
Existence and uniqueness for a nonlinear fractional differential equation
-
Delbosco D., and Rodino L. Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204 (1996) 609-625
-
(1996)
J. Math. Anal. Appl.
, vol.204
, pp. 609-625
-
-
Delbosco, D.1
Rodino, L.2
-
29
-
-
0037081673
-
Analysis of fractional differential equations
-
Diethelm K., and Ford N.J. Analysis of fractional differential equations. J. Math. Anal. Appl. 265 (2002) 229-248
-
(2002)
J. Math. Anal. Appl.
, vol.265
, pp. 229-248
-
-
Diethelm, K.1
Ford, N.J.2
-
30
-
-
53949111458
-
Basic theory of fractional differential equations
-
Lakshmikantham V., and Vatsala A.S. Basic theory of fractional differential equations. Nonlinear Anal. TMA 69 8 (2008) 2677-2682
-
(2008)
Nonlinear Anal. TMA
, vol.69
, Issue.8
, pp. 2677-2682
-
-
Lakshmikantham, V.1
Vatsala, A.S.2
-
31
-
-
33845961350
-
Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives
-
Daftardar-Gejji V. Analysis of a system of nonautonomous fractional differential equations involving Caputo derivatives. J. Math. Anal. Appl. 328 2 (2007) 1026-1033
-
(2007)
J. Math. Anal. Appl.
, vol.328
, Issue.2
, pp. 1026-1033
-
-
Daftardar-Gejji, V.1
-
32
-
-
34247394106
-
On systems of linear fractional differential equations with constant coefficients
-
Bonilla B., Rivero M., and Trujillo J.J. On systems of linear fractional differential equations with constant coefficients. Appl. Math. Comput. 187 1 (2007) 68-78
-
(2007)
Appl. Math. Comput.
, vol.187
, Issue.1
, pp. 68-78
-
-
Bonilla, B.1
Rivero, M.2
Trujillo, J.J.3
-
33
-
-
0002731965
-
Stability results of fractional differential equations with applications to control processing
-
Lille, France
-
D. Matignon, Stability results of fractional differential equations with applications to control processing, in: Proceeding of IMACS, IEEE-SMC, Lille, France (1996) pp. 963-968
-
(1996)
Proceeding of IMACS, IEEE-SMC
, pp. 963-968
-
-
Matignon, D.1
-
34
-
-
33947133956
-
Stability analysis of linear fractional differential system with multiple time delays
-
Deng W., Li C., and Lü J. Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynam. 48 (2007) 409-416
-
(2007)
Nonlinear Dynam.
, vol.48
, pp. 409-416
-
-
Deng, W.1
Li, C.2
Lü, J.3
-
35
-
-
57649105528
-
A note on the stability of fractional order systems
-
Tavazoei M.S., and Haeri M. A note on the stability of fractional order systems. Math. Comput. Simulation. 79 5 (2009) 1566-1576
-
(2009)
Math. Comput. Simulation.
, vol.79
, Issue.5
, pp. 1566-1576
-
-
Tavazoei, M.S.1
Haeri, M.2
-
36
-
-
74149083579
-
-
I. Petrás ̌, Stability of fractional-order systems with rational orders
-
I. Petrás ̌, Stability of fractional-order systems with rational orders
-
-
-
-
37
-
-
34250661428
-
Numerical approach to differential equations of fractional order
-
Momani S., and Odibat Z. Numerical approach to differential equations of fractional order. J. Comput. Appl. Math. 207 1 (2007) 96-110
-
(2007)
J. Comput. Appl. Math.
, vol.207
, Issue.1
, pp. 96-110
-
-
Momani, S.1
Odibat, Z.2
-
38
-
-
38649111984
-
Further accuracy tests on Adomian decomposition method for chaotic systems
-
Abdulaziz O., Noor N., and M I. Further accuracy tests on Adomian decomposition method for chaotic systems. Chaos Solitons Fractals 36 5 (2008) 1405-1411
-
(2008)
Chaos Solitons Fractals
, vol.36
, Issue.5
, pp. 1405-1411
-
-
Abdulaziz, O.1
Noor, N.2
M, I.3
-
39
-
-
33847067879
-
Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?
-
Wang Y., and Li C. Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle?. Phys. Lett. A 363 (2007) 414-419
-
(2007)
Phys. Lett. A
, vol.363
, pp. 414-419
-
-
Wang, Y.1
Li, C.2
-
40
-
-
0041384356
-
Chaotic dynamics of the fractional Lorenz system
-
Grigorenko I., and Grigorenko E. Chaotic dynamics of the fractional Lorenz system. Phys. Rev. Lett. 91 3 (2003) 034101
-
(2003)
Phys. Rev. Lett.
, vol.91
, Issue.3
, pp. 034101
-
-
Grigorenko, I.1
Grigorenko, E.2
-
41
-
-
18844427587
-
Chaos synchronization of the fractional Lü system
-
Deng W.H., and Li C.P. Chaos synchronization of the fractional Lü system. Physica A 353 (2005) 61-72
-
(2005)
Physica A
, vol.353
, pp. 61-72
-
-
Deng, W.H.1
Li, C.P.2
-
42
-
-
23144435914
-
A note on the fractional-order Chen system
-
Lu J.G., and Chen G. A note on the fractional-order Chen system. Chaos Solitons Fractals 27 3 (2006) 685-688
-
(2006)
Chaos Solitons Fractals
, vol.27
, Issue.3
, pp. 685-688
-
-
Lu, J.G.1
Chen, G.2
-
43
-
-
84977255207
-
Linear models of dissipation whose Q is almost frequency independent, Part II
-
Caputo M. Linear models of dissipation whose Q is almost frequency independent, Part II. J. Roy. Astr. Soc. 13 (1967) 529-539
-
(1967)
J. Roy. Astr. Soc.
, vol.13
, pp. 529-539
-
-
Caputo, M.1
-
45
-
-
0002847893
-
Fractional calculus: Integral and differential equations of fractional order
-
Carpinteri, Mainardi Eds, New York
-
R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, in: Carpinteri, Mainardi (Eds.), Fractals and fractional calculus, New York, 1997
-
(1997)
Fractals and fractional calculus
-
-
Gorenflo, R.1
Mainardi, F.2
-
46
-
-
0009450297
-
-
Freie Universitaet, Berlin
-
R. Gorenflo, F. Mainardi, Fractional oscillation and Mittag-Leffler functions, Fachbereich Mathematik and Informatic, A14/96, Freie Universitaet, Berlin, 1996, pp. 1-22
-
(1996)
Fractional oscillation and Mittag-Leffler functions, Fachbereich Mathematik and Informatic, A14/96
, pp. 1-22
-
-
Gorenflo, R.1
Mainardi, F.2
|