Matrix approach to discretization of fractional derivatives and to solution of fractional differential equations and their systems

A convenient method that enables easy discretization of fractional differential differential equations and their systems is described and illustrated on numerical solution of various types of fractional differential equations. The suggested method is the development of Podlubny´s matrix approach (Podlubny I., Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, 359-386; Podlubny I. et al., Journal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137-3153). In this article the method is further extended to solving systems of fractional differential equations and to discretizing fractional derivatives on non-equidistant nodes. The MAT-LAB toolbox that provides the method implementation and the sample code used to solve the examples have been developed.