Solving Binary Systems of Fractional Integro-Differential Equations by Taylor ‎Wavelets

In this paper, we give a new approach based on Taylor wavelets to solve fractional binary systems of integro-differential equations (FIDEs). To do this, first, we present the function approximation by using Taylor wavelets as well as the operational matrix of fractional integration of these wavelets. Then, by approximating the fractional derivatives of the solutions of the main problem in terms of the Taylor wavelets and using the operational matrix of fractional integration, we approximate the solutions of the main problem. By substituting these approximations in the FIDEs, we obtain a system of nonlinear algebraic equations. Finally, by the help of the proposed method, we solve some numerical examples and show the accuracy and applicability of the method‎.‎