An approximate approach for fractional singular delay integro-differential equations

Narges Peykrayegan; Mehdi Ghovatmand; Mohammad Hadi Noori Skandari; Dumitru Baleanu; Narges Peykrayegan; Mehdi Ghovatmand; Mohammad Hadi Noori Skandari; Dumitru Baleanu

doi:10.3934/math.2022507

AIMS Mathematics

2022, Volume 7, Issue 5: 9156-9171. doi: 10.3934/math.2022507

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An approximate approach for fractional singular delay integro-differential equations

1.
Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
2.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
3.
Institute of Space Sciences, Magurele-Bucharest, Romania
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 07 December 2021 Revised: 18 February 2022 Accepted: 20 February 2022 Published: 09 March 2022
MSC : 26A33, 34K37, 45G05

In this article, we present Jacobi-Gauss collocation method to numerically solve the fractional singular delay integro-differential equations, because such methods have better superiority, capability and applicability than other methods. We first apply a technique to replace the delay function in the considered equation and suggest an equivalent system. We then propose a Jacobi-Gauss collocation approach to discretize the obtained system and to achieve an algebraic system. Having solved the algebraic system, an approximate solution is gained for the original equation. Three numerical examples are solved to show the applicability of presented approximate approach. Obtaining the approximations of the solution and its fractional derivative simultaneously and an acceptable approximation by selecting a small number of collocation points are advantages of the suggested method.
Citation: Narges Peykrayegan, Mehdi Ghovatmand, Mohammad Hadi Noori Skandari, Dumitru Baleanu. An approximate approach for fractional singular delay integro-differential equations[J]. AIMS Mathematics, 2022, 7(5): 9156-9171. doi: 10.3934/math.2022507

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Abstract

In this article, we present Jacobi-Gauss collocation method to numerically solve the fractional singular delay integro-differential equations, because such methods have better superiority, capability and applicability than other methods. We first apply a technique to replace the delay function in the considered equation and suggest an equivalent system. We then propose a Jacobi-Gauss collocation approach to discretize the obtained system and to achieve an algebraic system. Having solved the algebraic system, an approximate solution is gained for the original equation. Three numerical examples are solved to show the applicability of presented approximate approach. Obtaining the approximations of the solution and its fractional derivative simultaneously and an acceptable approximation by selecting a small number of collocation points are advantages of the suggested method.

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