Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.