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Application of modified decomposition method for the analytical solution of space fractional diffusion equation. (English) Zbl 1133.65119

Summary: Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by a modified decomposition method. By using initial conditions, the explicit solutions of the equations are presented in the closed form. The decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self-cancelling “noise” phenomenon. Two examples, the first one is the one-dimensional and the second one is the two-dimensional fractional diffusion equation, are presented to show the application of the present technique. The present method performs extremely well in terms of efficiency and simplicity.

MSC:

65R20 Numerical methods for integral equations
26A33 Fractional derivatives and integrals
45K05 Integro-partial differential equations
35K15 Initial value problems for second-order parabolic equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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