Application of Fractional Order Legendre Polynomials: a New Procedure for Solution of Linear and Nonlinear Fractional Differential Equations under $m$-point Nonlocal Boundary Conditions

Abstract

In this paper, we have proposed a new formulation for the solution of a general class of fractional differential equations (linear and nonlinear) under $\hat{m}$-point boundary conditions. We derive some new operational matrices and based on these operational matrices we develop scheme to approximate solution of the problem. The scheme convert the boundary value problem to a system of easily solvable algebraic equations. We show the applicability of the scheme by solving some test problems. The scheme is computer oriented.