Numerical treatment of non-integer order partial differential equations by omitting discretization of data

Abstract

In this manuscript, we derived the shifted Jacobi operational matrices of fractional derivatives and integration which are applied for numerical solution of general linear multi-term fractional partial differential equations (FPDEs). A new approach implementing shifted Jacobi operational matrix without using the shifted Jacobi collocation technique is introduced for the numerical solution of multi-term FPDEs. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. Further the proposed method needs no discretization of data. The proposed method is applied for solving linear multi-term FPDEs subject to initial conditions and the approximate solutions are obtained for some tested problems. Special attention is given to the comparison of the numerical results obtained by the considered method with those found by other known methods like homotopy analysis (HAM) method. For computation purposes, we use Matlab 2016.