New operational matrix of derivative for solving non-linear fractional differential equations via Genocchi polynomials

Abstract

In this research, new operational method based on Genocchi polynomials for numerical solutions of non-linear fractional differential equations (NFDEs) is proposed. The Genocchi operational matrix of fractional derivative is first constructed by using some important properties of Genocchi polynomials. These operational matrices together with the collocation method are used to reduce the NFDEs into a system of non-linear algebraic equations. The error bound for this proposed method is shown. Some examples are given to display the simplicity and accuracy of the proposed technique. Keywords: Genocchi polynomials, Operational matrix of fractional derivatives, Fractional differential equations, Collocation points, 2010 MSC: 0096-3003