Khader, M.M. (2012) Introducing an Efficient Modification of the Homotopy Perturbation Method by Using Chebyshev Polynomials. Arab Journal of Mathematical Sciences, 18, 61-71.

has been cited by the following article:

• TITLE: Chebyshev Pseudo-Spectral Method for Solving Fractional Advection-Dispersion Equation

  AUTHORS: N. H. Sweilam, M. M. Khader, M. Adel

  KEYWORDS: Fractional Advection-Dispersion Equation, Caputo Fractional Derivative, Finite Difference Method, Chebyshev Pseudo-Spectral Method, Convergence Analysis

  JOURNAL NAME: Applied Mathematics, Vol.5 No.19, November 18, 2014

  ABSTRACT: Fractional differential equations have recently been applied in various areas 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 Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.