Matrix Approach to Discretization of Ordinary and Partial Differential Equations of Arbitrary Real Order: The Matlab Toolbox

Abstract

The method developed recently by Podlubny et al. (I. Podlubny, Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, pp. 359–386; I. Podlubny et al., Journal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137–3153) makes it possible to immediately obtain the discretization of ordinary and partial differential equations by replacing the derivatives with their discrete analogs in the form of triangular strip matrices. This article presents a Matlab toolbox that implements the matrix approach and allows easy and convenient discretization of ordinary and partial differential equations of arbitrary real order. The basic use of the functions implementing the matrix approach to discretization of derivatives of arbitrary real order (so-called fractional derivatives, or fractional-order derivatives), and to solution of ordinary and partial fractional differential equations, is illustrated by examples with explanations.