Geodesic
An Approximate Approach for Systems of Fractional Integro-Differential Equations Based on Taylor Expansion
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 3, p. 379 .

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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 the extit{m}th-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.
Classification : 65R20 34A08
Keywords: Fractional differential equation (FDE), systems of fractional integro-differential equations (SFIDE), Riemann-Liouville fractional derivative, Taylor expansion, error analysis 
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     author = {M. Didgar and A. R. Vahidi and J. Biazar},
     title = {An {Approximate} {Approach} for {Systems} of {Fractional} {Integro-Differential} {Equations} {Based} on {Taylor} {Expansion}},
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M. Didgar; A. R. Vahidi; J. Biazar. An Approximate Approach for Systems of Fractional Integro-Differential Equations Based on Taylor Expansion. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 3, p. 379 . http://geodesic.mathdoc.fr/item/KJM_2020_44_3_a3/