New collocation scheme for solving fractional partial differential equations

Abstract

This article concerned about the numerical solution of time fractional partial differential equations (FPDEs). The proposed technique is using shifted Chebyshev-Gauss-Lobatto (CGL) collocation points in conjunction with an operational matrix of Caputo sense derivatives via Genocchi polynomials. The system of linear algebraic equations is obtained when the main equation along with the initial as well as boundary conditions is collocated by using shifted CGL collocation points. The main approach to this method is to transform the FPDEs to system of algebraic equations, hence, greatly simplify the numerical scheme. Comparison of the obtained results with the existing methods depicts that the suggested method is highly effect, more efficient and have less computational work. Some examples are given to illustrate the effectiveness and applicability of the proposed technique.