Numerical studies for solving System of Linear Fractional Integro-Differential Equations by using least squares method and shifted Chebyshev polynomials of the third kind method

In this paper, a new numerical method for solving a linear system of fractional integro- differential equations is presented. The fractional derivative is considered in the Caputo sense. The method is least squares method aid of shifted Chebyshev polynomials of the third kind method introduced roposed . The suggested method reduces this type of system to the solution of system 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 All results are obtained by using Mathematics 10 programming.