A fractional-order operational method for numerical treatment of multi-order fractional partial differential equation with variable coefficients

Abstract

In this paper, generalized fractional-order Legendre functions (GFLFs) are used to introduce a new operational-projection method for numerical solution of a class of partial differential equations. To this end, GFLFs-operational matrix of fractional integration is derived and apply to reduce a multi-order time-space-fractional convection–diffusion equations with variable coefficients, subject to initial-boundary conditions, to a system of algebraic equations. Numerical examples illustrate the validity, accuracy and applicability of the method. For the evaluation, comparison with some numerical methods shows that the proposed method is accurate.