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Zbl 1221.65263
Khader, M.M.
On the numerical solutions for the fractional diffusion equation. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 6, 2535-2542 (2011). ISSN 1007-5704

Summary: Fractional differential equations have recently been applied in various area of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional diffusion equation (FDE) is considered. The fractional derivative is described in the Caputo sense. The method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FDE to a system of ordinary differential equations, which solved by the finite difference method. Numerical simulation of FDE is presented and the results are compared with the exact solution and other methods.

MSC 2000:: *65M70 Spectral, collocation and related methods (IVP of PDE)
35R11
26A33 Fractional derivatives and integrals (real functions)
35K20 Second order parabolic equations, boundary value problems
45K05 Integro-partial differential equations

Keywords: finite difference method; fractional diffusion equation; Chebyshev polynomials; Caputo derivative

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Zentralblatt MATH Berlin [Germany]