Analytical solution of a fractional diffusion equation by Adomian decomposition method

Applied Mathematics and Computation

Volumn 174, Issue 1, 2006, Pages 329-336

  Saha Ray, S ^a   Bera, R K ^b  

^a B P PODDAR INSTITUTE OF MANAGEMENT AND TECHNOLOGY   (India)

^b HERITAGE INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Adomian decomposition method; Fractional derivative; Fractional differential equation; Fractional diffusion equation

Indexed keywords

DECOMPOSITION; NONLINEAR EQUATIONS; NUMERICAL METHODS;

ADOMIAN DECOMPOSITION METHOD; FRACTIONAL DERIVATIVE; FRACTIONAL DIFFERENTIAL EQUATION; FRACTIONAL DIFFUSION EQUATION;

DIFFUSION;

EID: 33344463928     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.04.082     Document Type: Article

References (36)

1. K. Diethelm An algorithm for the numerical solution of differential equations of fractional order Elec. Trans. Numer. Anal. 5 1997 1 6
2. K. Diethelm, A.D. Freed, The FracPECE subroutine for the numerical solution of differential equations of fractional order, in: S. Heinzel, T. Plesser (Eds.), GWDG-Berichte, Forschung und wissenschaftliches Rechnen: Beiträge zum Heinz-Billing-Preis 1998 (No. 52), Gesellschaft für wissenschaftliche Datenverarbeitung, Göttingen, 1999, pp. 57-71.
3. K. Diethelm, and N.J. Ford Analysis of fractional differential equations J. Math. Anal. Appl. 265 2002 229 248
4. K. Diethelm, N.J. Ford, and A.D. Freed A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 2002 3 22
5. K. Diethelm, and N.J. Ford Numerical solution of the Bagley-Torvik equation Bit Numer. Math. 42 3 2002 490 507
6. K. Diethelm, and A.D. Ford On the solution of nonlinear fractional-order differential equations used in the modeling of viscoplasticity F. Keil W. Mackens H. Voß J. Werther Scientific computing in chemical engineering II. Computational fluid dynamics, reaction engineering, and molecular properties 1999 Springer-Verlag Heidelberg 217 224
7. K. Diethelm, and N.J. Ford The numerical solution of linear and nonlinear fractional differential equations involving fractional derivatives of several orders Numerical analysis report vol. 379 2001 Manchester Centre for Computational Mathematics Manchester, England
8. R. Gorenflo, E.A. Abdel-Rehim, Approximation of time-fractional diffusion with central drift by difference schemes, Berlin Free University, 2003. Available from: 〈 http://www.math.fu-berlin.de/publ/index.html〉.
9. R. Gorenflo, and F. Mainardi Fractional calculus and stable probability distributions Arch. Mech. 50 1998 377 388
10. F. Mainardi Fractional relaxation-oscillation and fractional diffusion-wave phenomena Chaos Soliton Fract. 7 9 1996 1461 1477
11. R. Gorenflo, Y. Luchko, and F. Mainardi Wright functions as scale-invariant solutions of the diffusion-wave equation J. Comput. Appl. Math. 118 2000 175 191
12. F. Mainardi, and G. Pagnini The Wright functions as solutions of the time-fractional diffusion equation Appl. Math. Comput. 141 2003 51 62
13. G. Adomian Nonlinear stochastic systems theory and applications to physics 1989 Kluwer Academic Publishers Netherlands
14. G. Adomian Solving frontier problems of physics: the decomposition method 1994 Kluwer Academic Publishers Boston
15. G. Adomian An analytical solution of the stochastic Navier-Stokes system Found. Phys. 21 7 1991 831 843
16. G. Adomian, and R. Rach Linear and nonlinear Schrödinger equations Found. Phys. 21 1991 983 991
17. G. Adomian Solution of physical problems by decomposition Comput. Math. Appl. 27 9/10 1994 145 154
18. G. Adomian Solutions of nonlinear P.D.E. Appl. Math. Lett. 11 3 1998 121 123
19. K. Abbaoui, and Y. Cherruault The decomposition method applied to the Cauchy problem Kybernetes 28 1999 103 108
20. D. Kaya, and A. Yokus A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equations Math. Comput. Simul. 60 6 2002 507 512
21. A. Wazwaz A reliable modification of Adomian decomposition method Appl. Math. Comput. 102 1 1999 77 86
22. D. Kaya, and S.M. El-Sayed On a generalized fifth order KdV equations Phys. Lett. A 310 1 2003 44 51
23. D. Kaya, and S.M. El-Sayed An application of the decomposition method for the generalized KdV and RLW equations Chaos Soliton Fract. 17 5 2003 869 877
24. D. Kaya An explicit and numerical solutions of some fifth-order KdV equation by decomposition method Appl. Math. Comput. 144 2-3 2003 353 363
25. D. Kaya A numerical simulation of solitary-wave solutions of the generalized regularized long-wave equation Appl. Math. Comput. 149 3 2004 833 841
26. A.J. George, and A. Chakrabarti The Adomian method applied to some extraordinary differential equations Appl. Math. Lett. 8 3 1995 91 97
27. H.L. Arora, and F.I. Abdelwahid Solutions of non-integer order differential equations via the Adomian decomposition method Appl. Math. Lett. 6 1 1993 21 23
28. N.T. Shawagfeh The decomposition method for fractional differential equations J. Frac. Calc. 16 1999 27 33
29. N.T. Shawagfeh Analytical approximate solutions for nonlinear fractional differential equations Appl. Math. Comput. 131 2002 517 529
30. S. Saha Ray, and R.K. Bera Solution of an extraordinary differential equation by Adomian decomposition method J. Appl. Math. 4 2004 331 338
31. S. Saha Ray, and R.K. Bera Analytical solution of a dynamic system containing fractional derivative of order 1/2 by Adomian decomposition method Trans. ASME J. Appl. Mech. 72 2 2005 290 295
32. S. Saha Ray, R.K. Bera, An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2004.07.020.
33. S. Saha Ray, R.K. Bera, Analytical solution of the Bagley Torvik equation by Adomian decomposition method, Appl. Math. Comput., in press, doi:10.1016/j.amc.2004.09.006.
34. I. Podlubny Fractional differential equations 1999 Academic Press San Diego, CA
35. K.B. Oldham, and J. Spanier The fractional calculus 1974 Academic Press New York and London
36. S. Wolfram, Mathematica for Windows, Version 5.0, Wolfram Research, 2003.