Numerical Identification of the Fractional Derivatives in the Two-Dimensional Fractional Cable Equation

Abstract

In this paper, the two-dimensional fractional cable equation is considered, an efficient numerical method to obtain the identification of the fractional derivatives is investigated. Concerning the numerical treatment of the two-dimensional fractional cable equation, a fourth-order compact finite difference method is proposed, the stability and convergence of the compact difference method are discussed rigorously by means of the Fourier method. For the inverse problem of the identification of the fractional derivatives, Levenberg---Marquardt iterative method is employed, and the fractional sensitivity equation is obtained by means of the digamma function. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.