A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems

Abstract

Abstract We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n ∈ ℕ. The Bernstein polynomials (BPs) are redefined in a fractional form over an arbitrary interval [a, b]. Theoretical results related to the ractional Bernstein polynomials (FBPs) are proven. The well-known shooting technique is extended for the numerical treatment of nonlinear fractional boundary value problems of arbitrary order. The initial value problems were solved using a collocation method with collocation points at the location of the local maximum of the FBPs. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.