An efficient Numerical Approach for solving Nonlinear Two-Point Boundary Value Problems with a Caputo Fractional Derivatives

Abstract

We propose an efficient numerical method to solve the nonlinear two-point boundary value problems of Caputo fractional derivative based on the nonlinear Shooting method. The two-point BVP is transformed into the system of IVP with an unknown guess. The initial guess is updated by solving Newton's and the Hally's method combined with another boundary condition. Each of the method have second and third order convergence, respectively. Numerical illustrations show the efficiency of the proposed method