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The main purpose of this work is to present an efficient approximate approach for solving linear systems of fractional integro-differential equations based on a new application of Taylor expansion. Using themth-order Taylor polynomial for unknown functions and employing integration method the given system of fractional integro-differential equations will be converted into a system of linear equations with respect to unknown functions and their derivatives. The solutions of this system yield the approximate solutions of fractional integro-differential equations system. The Riemann-Liouville fractional derivative is applied in calculations. An error analysis is discussed as well. The accuracy and the efficiency of the suggested method is illustrated by considering five numerical examples.

An Approximate Approach for Systems of Fractional IntegroDifferential Equations Based on Taylor Expansion