A Numerical Scheme for Solving Nonlinear Boundary Value Problems of Fractional Order 0 ≤ β ≤ α < 1

The primary objective of this research work is to find accurate numerical approximations for nonlinear fractional order boundary value problems (BVPs). To carry out this goal, central finite difference scheme of order four is used to approximate first- and second-order derivatives. Integrals are approximated using composite Trapezoidal rule in "the Caputo definition". The effectiveness of the proposed scheme is illustrated by solving nonlinear fractional order BVPs of order 0 ≤ β ≤ α < 1. (author)