### An Approximate Approach for Systems of Fractional Integro- Differential Equations Based on Taylor Expansion

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**Authors:**M. DIDGAR, A. R. VAHIDI AND J. BIAZAR

**DOI:**10.46793/KgJMat2003.379D

**Abstract:**

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 the mth-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.

**Keywords:**

Fractional diﬀerential equation (FDE), systems of fractional integro-diﬀerential equations (SFIDE), Riemann-Liouville fractional derivative, Taylor expansion, error analysis.

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