### Journals Information

Mathematics and Statistics Vol. 9(5), pp. 792 - 798
DOI: 10.13189/ms.2021.090519
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## The Fractional Residual Power Series Method for Solving a System of Linear Fractional Fredholm Integro-differential Equations

Prapart Pue-on *
Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand

ABSTRACT

In this manuscript, the fractional residual power series (FRPS) method is employed in solving a system of linear fractional Fredholm integro-differential equations. The significant role of this system in various fields has attracted the attention of researchers for a decade. The definition of fractional derivative here is described in the Caputo sense. The proposed method relies on the generalized Taylor series expansion as well as the fact that the fractional derivative of stationary is zero. The process starts by constructing a residual function by supposing the finite order of an approximate power series solution that prescribes the initial conditions. Then, utilizing some conditions, the residual functions are converted to a linear system for the power series coefficients. Solving the linear system reveals the coefficients of the fractional power series solution. Finally, by substituting these coefficients into the supposed form of a solution, the approximate fractional power series solutions are derived. This technique has the advantage of being able to be applied directly to the problem and spending less time on computation. It is not only an easy method for implementation of the problem, but also provides productive results after a few iterations. Some problems with known solutions emphasize the procedure's simplicity and reliability. Moreover, the obtained exact solution demonstrated the efficiency and accuracy of the presented method.

KEYWORDS
Fractional Fredholm Integro-differential Equations, Caputo Fractional Derivatives, Residual Power Series Method, Exact Solution

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Prapart Pue-on , "The Fractional Residual Power Series Method for Solving a System of Linear Fractional Fredholm Integro-differential Equations," Mathematics and Statistics, Vol. 9, No. 5, pp. 792 - 798, 2021. DOI: 10.13189/ms.2021.090519.

(b). APA Format:
Prapart Pue-on (2021). The Fractional Residual Power Series Method for Solving a System of Linear Fractional Fredholm Integro-differential Equations. Mathematics and Statistics, 9(5), 792 - 798. DOI: 10.13189/ms.2021.090519.