-
1
-
-
0035538580
-
Spectral analysis of fractional kinetic equations with random data
-
Anh, V.V. and Leonenko, N.N., 2001, " Spectral analysis of fractional kinetic equations with random data, " Journal of Statistical Physics 104 (5 / 6). 1349-1387.
-
(2001)
Journal of Statistical Physics
, vol.104
, Issue.5
, pp. 1349-1387
-
-
Anh, V.V.1
Leonenko, N.N.2
-
3
-
-
0001342751
-
On the existence of the order domain and the solution of distributed order equations, Part i
-
Bagley, R.L. and Torvik, P.J., 2000 a, " On the existence of the order domain and the solution of distributed order equations, Part I, " International Journal ofApplied Mathematics 2, 865-882.
-
(2000)
International Journal OfApplied Mathematics
, vol.2
, pp. 865-882
-
-
Bagley, R.L.1
Torvik, P.J.2
-
4
-
-
0001342751
-
On the existence of the order domain and the solution of distributed order equations, Part II
-
Bagley, R.L. and Torvik, P.J., 2000 b, " On the existence of the order domain and the solution of distributed order equations, Part II, " International Journal of Applied Mathematics 2, 965-987.
-
(2000)
International Journal of Applied Mathematics
, vol.2
, pp. 965-987
-
-
Bagley, R.L.1
Torvik, P.J.2
-
5
-
-
84977255207
-
Linear models of dissipation whose Q is almost frequency independent, Part II
-
Caputo, M., 1967, " Linear models of dissipation whose Q is almost frequency independent, Part II, " Geophysical Journal of the Royal Astronomical Society 13, 529-539.
-
(1967)
Geophysical Journal of the Royal Astronomical Society
, vol.13
, pp. 529-539
-
-
Caputo, M.1
-
7
-
-
51249169579
-
Mean fractional-order derivatives differential equations and filters," Annali della Universit di Ferrara (Sezione VII
-
Caputo, M., 1995, " Mean fractional-order derivatives differential equations and filters," Annali della Universit di Ferrara (Sezione VII, Scienze Mathematiche) 41, 73-84.
-
(1995)
Scienze Mathematiche
, vol.41
, pp. 73-84
-
-
Caputo, M.1
-
8
-
-
0000227056
-
Distributed order differential equations modelling dielectric induction and diffusion
-
Caputo, M., 2001, " Distributed order differential equations modelling dielectric induction and diffusion, " Fractional Calculus and Applied Analysis 4 (4). 421-442.
-
(2001)
Fractional Calculus and Applied Analysis
, vol.4
, Issue.4
, pp. 421-442
-
-
Caputo, M.1
-
9
-
-
51649182765
-
Linear models of dissipation in anelastic solids
-
Caputo, M. and Mainardi, F., 1971, " Linear models of dissipation in anelastic solids, " Rivista del Nuovo Cimento (Series II) 1, 161-198.
-
(1971)
Rivista Del Nuovo Cimento (Series II)
, vol.1
, pp. 161-198
-
-
Caputo, M.1
Mainardi, F.2
-
10
-
-
41349088572
-
Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations
-
Chechkin, A.V., Gorenflo, R., and Sokolov, I.M., 2002, " Retarding subdiffusion and accelerating superdiffusion governed by distributed-order fractional diffusion equations, " Physical Review E 66, 046129 / 1-6.
-
(2002)
Physical Review e
, vol.66
, pp. 1-6
-
-
Chechkin, A.V.1
Gorenflo, R.2
Sokolov, I.M.3
-
11
-
-
10344261735
-
Distributed order time fractional diffusion equation
-
Chechkin, A.V., Gorenflo, R., Sokolov, I.M., and Gonchar, V.Y., 2003 a, " Distributed order time fractional diffusion equation, " Fractional Calculus and Applied Analysis 6, 259-279.
-
(2003)
Fractional Calculus and Applied Analysis
, vol.6
, pp. 259-279
-
-
Chechkin, A.V.1
Gorenflo, R.2
Sokolov, I.M.3
Gonchar, V.Y.4
-
12
-
-
0041361963
-
Fractional Fokker-Planck equation for ultraslow kinetics
-
Chechkin, A.V., Klafter, J., and Sokolov, I.M., 2003 b, " Fractional Fokker-Planck equation for ultraslow kinetics, " Europhysics Letters 63, 326-332.
-
(2003)
Europhysics Letters
, vol.63
, pp. 326-332
-
-
Chechkin, A.V.1
Klafter, J.2
Sokolov, I.M.3
-
13
-
-
0012570827
-
Numerical solution methods for distributed order differential equations
-
Diethelm, K. and Ford, N.J., 2001, " Numerical solution methods for distributed order differential equations, " Fractional Calculus and Applied Analysis 4, 531-542.
-
(2001)
Fractional Calculus and Applied Analysis
, vol.4
, pp. 531-542
-
-
Diethelm, K.1
Ford, N.J.2
-
14
-
-
33748663764
-
Numerical solution of linear multi-term initial value problems of fractional order
-
Diethelm, K. and Luchko, Y., 2004, " Numerical solution of linear multi-term initial value problems of fractional order, " Computational Methods of Numerical Analysis 6, 243-263.
-
(2004)
Computational Methods of Numerical Analysis
, vol.6
, pp. 243-263
-
-
Diethelm, K.1
Luchko, Y.2
-
16
-
-
1942542248
-
Cauchy problem for fractional diffusion equations
-
Eidelman, S.D. and Kochubei, A.N., 2004, " Cauchy problem for fractional diffusion equations, " Journal of Differential Equations 199, 211-255.
-
(2004)
Journal of Differential Equations
, vol.199
, pp. 211-255
-
-
Eidelman, S.D.1
Kochubei, A.N.2
-
17
-
-
0001735487
-
Higher Transcendental Functions
-
Erdlyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F.G., 1955, Higher Transcendental Functions, McGraw-Hill, New York, Vol. 3, pp. 206-227.
-
(1955)
McGraw-Hill, New York
, vol.3
, pp. 206-227
-
-
Erdlyi, A.1
Magnus, W.2
Oberhettinger, F.3
Tricomi, F.G.4
-
18
-
-
0003421261
-
-
2nd Edition, Wiley, New York, Vol.
-
Feller, W., 1971, An Introduction to Probability Theory and its Applications, 2 nd Edition, Wiley, New York, Vol. 2.
-
(1971)
An Introduction to Probability Theory and Its Applications
, pp. 2
-
-
Feller, W.1
-
19
-
-
0003625475
-
-
Academic Press, New York, Vol. I.
-
Gelfand, I.M. and Shilov, G.E., 1964, Generalized Functions, Academic Press, New York, Vol. I.
-
(1964)
Generalized Functions
-
-
Gelfand, I.M.1
Shilov, G.E.2
-
21
-
-
0002847893
-
-
A. Carpinteri and F. Mainardi, eds., Springer Verlag, Vienna, pp.
-
Gorenflo, R. and Mainardi, F., 1997, " Fractional calculus: Integral and differential equations of fractional order," in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., Springer Verlag, Vienna, pp. 223-276. http://www.fracalmo.org
-
(1997)
Fractional Calculus: Integral and Differential Equations of Fractional Order," in Fractals and Fractional Calculus in Continuum Mechanics
, pp. 223-276
-
-
Gorenflo, R.1
Mainardi, F.2
-
22
-
-
33646113530
-
Simply and multiply scaled diffusion limits for continuous time random walks
-
Gorenflo, R. and Mainardi, F., 2005, " Simply and multiply scaled diffusion limits for continuous time random walks, " in Proceedings of the International Workshop on Chaotic Transport and Complexity in Fluids and Plasmas, S. Benkadda, X. Leoncini, and G. Zaslavsky, eds., Journal of Physics: Conference Series 7, 1-16.
-
Proceedings of the International Workshop on Chaotic Transport and Complexity in Fluids and Plasmas
-
-
Gorenflo, R.1
Mainardi, F.2
-
23
-
-
0001859930
-
Mapping between solutions of fractional diffusion-wave equations
-
Gorenflo, R., Iskenderov, A., and Luchko, Y., 2000 a, " Mapping between solutions of fractional diffusion-wave equations, " Fractional Calculus and Applied Analysis 3, 75-86.
-
(2000)
Fractional Calculus and Applied Analysis
, vol.3
, pp. 75-86
-
-
Gorenflo, R.1
Iskenderov, A.2
Luchko, Y.3
-
24
-
-
0000009397
-
Analytical properties and applications of the Wright function
-
Gorenflo, R., Luchko, Y., and Mainardi, F., 1999, " Analytical properties and applications of the Wright function, " Fractional Calculus and Applied Analysis 2, 383-414.
-
(1999)
Fractional Calculus and Applied Analysis
, vol.2
, pp. 383-414
-
-
Gorenflo, R.1
Luchko, Y.2
Mainardi, F.3
-
25
-
-
0000103589
-
Wright functions as scale-invariant solutions of the diffusion-wave equation
-
Gorenflo, R., Luchko, Y., and Mainardi, F., 2000 b, " Wright functions as scale-invariant solutions of the diffusion-wave equation, " Journal of Computational and Applied Mathematics 118, 175-191.
-
(2000)
Journal of Computational and Applied Mathematics
, vol.118
, pp. 175-191
-
-
Gorenflo, R.1
Luchko, Y.2
Mainardi, F.3
-
26
-
-
57249098754
-
Multi-dimensional solutions of time-fractional diffusion-wave equations
-
Hanyga, A., 2002, " Multi-dimensional solutions of time-fractional diffusion-wave equations, " Proceedings of the Royal Society A 458, 933-957.
-
(2002)
Proceedings of the Royal Society A
, vol.458
, pp. 933-957
-
-
Hanyga, A.1
-
27
-
-
0141892685
-
Fractional-order system identification based on continuous order-distributions
-
Hartley, T.T. and Lorenzo, C.F., 2003, " Fractional-order system identification based on continuous order-distributions, " Signal Processing 83, 2287-2300.
-
(2003)
Signal Processing
, vol.83
, pp. 2287-2300
-
-
Hartley, T.T.1
Lorenzo, C.F.2
-
29
-
-
33847309315
-
-
Elsevier, Amsterdam.
-
Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J., 2006, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
-
(2006)
Theory and Applications of Fractional Differential Equations
-
-
Kilbas, A.A.1
Srivastava, H.M.2
Trujillo, J.J.3
-
30
-
-
0000332009
-
Fractional-order diffusion
-
Kochubei, A.N., 1990, " Fractional-order diffusion, " Differential Equations 26, 485-492.
-
(1990)
Differential Equations
, vol.26
, pp. 485-492
-
-
Kochubei, A.N.1
-
31
-
-
33646371459
-
Solution of a modified fractional diffusion equation
-
Langlands, T.A.M., 2006, " Solution of a modified fractional diffusion equation, " Physica A 367, 136-144.
-
(2006)
Physica A
, vol.367
, pp. 136-144
-
-
Langlands, T.A.M.1
-
32
-
-
0036650957
-
Variable order and distributed order fractional operators
-
Lorenzo, C.F. and Hartley, T.T., 2002, " Variable order and distributed order fractional operators, " Nonlinear Dynamics 29, 57-98.
-
(2002)
Nonlinear Dynamics
, vol.29
, pp. 57-98
-
-
Lorenzo, C.F.1
Hartley, T.T.2
-
33
-
-
33845650781
-
-
Begell House, Redding, CT, p.
-
Magin, R.L., 2006, Fractional Calculus in Bioengineering, Begell House, Redding, CT, p. 684.
-
(2006)
Fractional Calculus in Bioengineering
, pp. 684
-
-
Magin, R.L.1
-
34
-
-
0001869174
-
-
S. Rionero and T. Ruggeri, eds., World Scientific, Singapore, pp.
-
Mainardi, F., 1993, " On the initial value problem for the fractional diffusion-wave equation," in Waves and Stability in Continuous Media, S. Rionero and T. Ruggeri, eds., World Scientific, Singapore, pp. 246-251.
-
(1993)
On the Initial Value Problem for the Fractional Diffusion-wave Equation," in Waves and Stability in Continuous Media
, pp. 246-251
-
-
Mainardi, F.1
-
35
-
-
0030464353
-
Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos
-
Mainardi, F., 1996, " Fractional relaxation-oscillation and fractional diffusion-wave phenomena," Chaos, Solitons and Fractals 7, 1461-1477.
-
(1996)
Solitons and Fractals
, vol.7
, pp. 1461-1477
-
-
Mainardi, F.1
-
36
-
-
0001983732
-
Fractional calculus: Some basic problems in continuum and statistical mechanics
-
Fractals and Fractional Calculus in Continuum Mechanics A. Carpinteri and F. Mainardi, eds., Springer Verlag, Berlin, pp.
-
Mainardi, F., 1997, " Fractional calculus: Some basic problems in continuum and statistical mechanics," in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, eds., CISM Courses and Lecture Notes, Vol. 378, Springer Verlag, Berlin, pp. 291-348. http://www.fracalmo.org
-
(1997)
CISM Courses and Lecture Notes
, pp. 291-348
-
-
Mainardi, F.1
-
37
-
-
0000145521
-
On Mittag-Leffler type functions in fractional evolution processes
-
Mainardi, F. and Gorenflo, R., 2000, " On Mittag-Leffler type functions in fractional evolution processes, " Journal of Computational and Applied Mathematics 118, 283-299.
-
(2000)
Journal of Computational and Applied Mathematics
, vol.118
, pp. 283-299
-
-
Mainardi, F.1
Gorenflo, R.2
-
38
-
-
0037457788
-
The Wright functions as solutions of the time-fractional diffusion equations
-
Mainardi, F. and Pagnini, G., 2003, " The Wright functions as solutions of the time-fractional diffusion equations, " Applied Mathematics and Computation 141 (1). 51-62.
-
(2003)
Applied Mathematics and Computation
, vol.141
, Issue.1
, pp. 51-62
-
-
Mainardi, F.1
Pagnini, G.2
-
39
-
-
34547102267
-
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
-
Mainardi, F. and Pagnini, G., 2007, " The role of the Fox-Wright functions in fractional sub-diffusion of distributed order, " Journal of Computational andAppliedMathematics, 207 (2). 245-257.
-
(2007)
Journal of Computational AndAppliedMathematics
, vol.207
, Issue.2
, pp. 245-257
-
-
Mainardi, F.1
Pagnini, G.2
-
40
-
-
0001407424
-
The fundamental solution of the space-time fractional diffusion equation
-
Mainardi, F., Luchko, Y., and Pagnini, G., 2001, " The fundamental solution of the space-time fractional diffusion equation, " Fractional Calculus andAppliedAnalysis 4, 153-192. http://www.fracalmo.org
-
(2001)
Fractional Calculus AndAppliedAnalysis
, vol.4
, pp. 153-192
-
-
Mainardi, F.1
Luchko, Y.2
Pagnini, G.3
-
41
-
-
58149510910
-
-
K. Tas and D. Baleanu, eds., Springer Verlag, Berlin, pp.
-
Mainardi, F., Mura, A., Pagnini, G., and Gorenflo, R., 2006 a, " Sub-diffusion equations of fractional order and their fundamental solutions," in Mathematical Methods in Engineering, K. Tas and D. Baleanu, eds., Springer Verlag, Berlin, pp. 20-48.
-
(2006)
Sub-diffusion Equations of Fractional Order and Their Fundamental Solutions," in Mathematical Methods in Engineering
, pp. 20-48
-
-
Mainardi, F.1
Mura, A.2
Pagnini, G.3
Gorenflo, R.4
-
42
-
-
34247367101
-
Some aspects of fractional diffusion equations of single and distributed order
-
Mainardi, F., Pagnini, G., and Gorenflo, R., 2006 b, " Some aspects of fractional diffusion equations of single and distributed order, " Applied Mathematics and Computation, 187 (1). 295-305.
-
(2006)
Applied Mathematics and Computation
, vol.187
, Issue.1
, pp. 295-305
-
-
Mainardi, F.1
Pagnini, G.2
Gorenflo, R.3
-
43
-
-
14844347453
-
Fox H functions in fractional diffusion
-
Mainardi, F., Pagnini, G., and Saxena, R.K., 2005, " Fox H functions in fractional diffusion, " Journal of Computational and Applied Mathematics 178 (1-2). 321-331.
-
(2005)
Journal of Computational and Applied Mathematics
, vol.178
, Issue.1
, pp. 321-331
-
-
Mainardi, F.1
Pagnini, G.2
Saxena, R.K.3
-
44
-
-
0002641421
-
The random walk's guide to anomalous diffusion: A fractional dynamics approach
-
Metzler, R. and Klafter, J., 2000, " The random walk's guide to anomalous diffusion: A fractional dynamics approach, " Physics Reports 339, 1-77.
-
(2000)
Physics Reports
, vol.339
, pp. 1-77
-
-
Metzler, R.1
Klafter, J.2
-
45
-
-
43949160695
-
Fractional model equation for anomalous diffusion
-
Metzler, R., Glckle, W.G., and Nonnenmacher, T.F., 1994, " Fractional model equation for anomalous diffusion, " Physica A 211, 13-24.
-
(1994)
Physica A
, vol.211
, pp. 13-24
-
-
Metzler, R.1
Glckle, W.G.2
Nonnenmacher, T.F.3
-
47
-
-
4544299160
-
Distributed order fractional subdiffusion
-
Naber, M., 2004, " Distributed order fractional subdiffusion, " Fractals 12 (1). 23-32.
-
(2004)
Fractals
, vol.12
, Issue.1
, pp. 23-32
-
-
Naber, M.1
-
49
-
-
0000599032
-
Fractional kinetic equations: Solutions and applications
-
764
-
Saichev, A. and Zaslavsky, G.M., 1997, " Fractional kinetic equations: Solutions and applications, " Chaos 7, 753-764.
-
(1997)
Chaos
, vol.7
-
-
Saichev, A.1
Zaslavsky, G.M.2
-
50
-
-
0003598080
-
-
Gordon and Breach, New York.
-
Samko, S.G., Kilbas, A.A., and Marichev, O.I., 1993, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York.
-
(1993)
Fractional Integrals and Derivatives: Theory and Applications
-
-
Samko, S.G.1
Kilbas, A.A.2
Marichev, O.I.3
-
51
-
-
0001553919
-
Fractional diffusion and wave equations
-
Schneider, W.R. and Wyss, W., 1989, " Fractional diffusion and wave equations, " Journal of Mathematical Physics 30, 134-144.
-
(1989)
Journal of Mathematical Physics
, vol.30
, pp. 134-144
-
-
Schneider, W.R.1
Wyss, W.2
-
52
-
-
31144434675
-
From diffusion to anomalous diffusion: A century after Einstein's Brownian motion
-
Sokolov, I.M. and Klafter, J., 2005, " From diffusion to anomalous diffusion: A century after Einstein's Brownian motion, " Chaos 15, 026103-026109.
-
(2005)
Chaos
, vol.15
, pp. 026103-026109
-
-
Sokolov, I.M.1
Klafter, J.2
-
53
-
-
2442679060
-
Distributed-order fractional kinetics
-
Sokolov, I.M., Chechkin, A.V., and Klafter, J., 2004, " Distributed-order fractional kinetics, " Acta Physica Polonica 35, 1323-1341.
-
(2004)
Acta Physica Polonica
, vol.35
, pp. 1323-1341
-
-
Sokolov, I.M.1
Chechkin, A.V.2
Klafter, J.3
-
54
-
-
32044453310
-
Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations: Part one
-
Umarov, S. and Gorenflo, R., 2005, " Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations: Part one, " Zeitschrift fr Analysis und ihre Anwendungen 24 (3). 449-466.
-
(2005)
Zeitschrift Fr Analysis und Ihre Anwendungen
, vol.24
, Issue.3
, pp. 449-466
-
-
Umarov, S.1
Gorenflo, R.2
-
55
-
-
0004315248
-
-
Springer Verlag, New York.
-
West, B.J., Bologna, M., and Grigolini, P., 2003, Physics of Fractal Operators, Springer Verlag, New York.
-
(2003)
Physics of Fractal Operators
-
-
West, B.J.1
Bologna, M.2
Grigolini, P.3
-
56
-
-
0036887936
-
Chaos, fractional kinetics and anomalous transport
-
Zaslavsky, G.M., 2002, " Chaos, fractional kinetics and anomalous transport, " Physics Reports 371, 461-580.
-
(2002)
Physics Reports
, vol.371
, pp. 461-580
-
-
Zaslavsky, G.M.1
|