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Analytical solution for the space fractional diffusion equation by two-step Adomian decomposition method. (English) Zbl 1221.65284

Summary: Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical superdiffusive problems in fluid flow, finance and other areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by two-step Adomian decomposition method (TSADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form and then their solutions have been represented graphically. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present technique. The solutions obtained by the standard decomposition method have been numerically evaluated and presented in the form of tables and then compared with those obtained by TSADM. The present TSADM performs extremely well in terms of efficiency and simplicity.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K57 Reaction-diffusion equations
35A25 Other special methods applied to PDEs
35C05 Solutions to PDEs in closed form
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