Analytical solution of a fractional diffusion equation by variational iteration method

Computers and Mathematics with Applications

Volumn 57, Issue 3, 2009, Pages 483-487

  Das, S ^a  

^a BANARAS HINDU UNIVERSITY   (India)

Author keywords

Analytical approximate solution; Fractional diffusion equation; Mittag Leffler function; Variational iteration method

Indexed keywords

DIFFUSION; OSCILLATORS (MECHANICAL); PARTICLE SIZE ANALYSIS;

ANALYTICAL APPROXIMATE SOLUTION; ANALYTICAL SOLUTIONS; EXPLICIT SOLUTIONS; FRACTIONAL DIFFUSION EQUATION; INITIAL VALUES; ITERATION METHODS; MITTAG-LEFFLER FUNCTION; NUMERICAL RESULTS; PRESENT METHODS; RAPID CONVERGENCES; SERIES SOLUTIONS; VARIATIONAL ITERATION METHOD;

ITERATIVE METHODS;

EID: 58149263050     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.09.045     Document Type: Article

References (14)

1. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York and London
2. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (2003), John Willey and Sons, Inc., New York
3. Podlubry J. Fractional Differential Equations (1999), Academic Press, San Diego, California, USA
4. Diethelm K., and Ford N.J. Analysis of Fractional differential equations. J. Math. Anal. Appl. 265 (2002) 229-248
5. Diethelm K. An Algorithm for the numerical solutions of differential equations of Fractional order. Elec. Trans. Numer. 5 (1997) 1-6
6. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Engrg. 167 (1998) 57-68
7. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Engrg. 167 (1998) 69-73
8. He J.H. Variational Iteration Method - a kind of nonlinear analytical technique: Some examples. Internat. J. Nonlinear Mech. 34 (1999) 699-708
9. He J.H. Variational Iteration Method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
10. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 (2006) 1141-1191
11. Shawagfeh N.T. Analytical approximate solutions for nonlinear Fractional differential equations. Appl. Math. Comput. 131 (2002) 517-529
12. K. Diethelm, N.J. Ford, The numerical solutions of linear and nonlinear Fractional differential equations involving Fractional derivatives of several orders, Numerical Analysis Report, V.379, Manchester Centre for Computational Math., England, 2001
13. Momani S., and Odibat Z. Numerical comparison of methods for solving linear differential equations of Fractional order. Chaos Solutions Fractals 31 (2007) 1248-1255
14. Saha Ray S., and Bera R.K. Analytical solution of a Fractional diffusion equation by Adomian decomposition method. Appl. Math. Comput. 174 (2006) 329-336