A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform

Ahmad Qazza (), Aliaa Burqan and Rania Saadeh
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Aliaa Burqan: Department of Mathematics, Faculty of Sciences, Zarqa University, Zarqa 13110, Jordan
Rania Saadeh: Department of Mathematics, Faculty of Sciences, Zarqa University, Zarqa 13110, Jordan

Mathematics, 2021, vol. 9, issue 23, 1-14

Abstract: In this paper, we use the ARA transform to solve families of fractional differential equations. New formulas about the ARA transform are presented and implemented in solving some applications. New results related to the ARA integral transform of the Riemann-Liouville fractional integral and the Caputo fractional derivative are obtained and the last one is implemented to create series solutions for the target equations. The procedure proposed in this article is mainly based on some theorems of particular solutions and the expansion coefficients of binomial series. In order to achieve the accuracy and simplicity of the new method, some numerical examples are considered and solved. We obtain the solutions of some families of fractional differential equations in a series form and we show how these solutions lead to some important results that include generalizations of some classical methods.

Keywords: fractional derivative; fractional-order differential equations; Riemann-Liouville fractional integrals; gamma function; ARA transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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