Numerical approach for solving space fractional order diffusion equations using shifted Chebyshev polynomials of the fourth kind

Authors: NASSER HASSAN SWIELAM, ABD ELHAMEED MOHAMED NAGY, ADEL ABD ELAZIZ EL SAYED

Abstract: In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method. The finite difference method is used to reduce the equations obtained by our approach for a system of algebraic equations that can be efficiently solved. Numerical results obtained with our approach are presented and compared with the results obtained by other numerical methods. The numerical results show the efficiency of the proposed approach.

Keywords: Space fractional order diffusion equation, Caputo derivative, Chebyshev collocation method, finite difference method, Chebyshev polynomials of the fourth kind; Euler approximation

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