Numerical studies for solving fractional integro-differential equations

In this paper, we give a new numerical method for solving a linear system of fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. The proposed method is least squares method aid of Hermite polynomials. The suggested method reduces this type of systems to the solution of systems of linear algebraic equations. To demonstrate the accuracy and applicability of the presented method some test examples are provided. Numerical results show that this approach is easy to implement and accurate when applied to integro-differential equations. We show that the solutions approach to classical solutions as the order of the fractional derivatives approach.