Solving a class of variable order nonlinear fractional integral differential equations by using reproducing kernel function

Zhi-Yuan Li; Mei-Chun Wang; Yu-Lan Wang; Zhi-Yuan Li; Mei-Chun Wang; Yu-Lan Wang

doi:10.3934/math.2022716

AIMS Mathematics

2022, Volume 7, Issue 7: 12935-12951. doi: 10.3934/math.2022716

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Solving a class of variable order nonlinear fractional integral differential equations by using reproducing kernel function

Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China

Received: 10 February 2022 Revised: 30 April 2022 Accepted: 04 May 2022 Published: 06 May 2022
MSC : 65R20, 65L10

In this paper, reproducing kernel interpolation collocation method is explored for nonlinear fractional integral differential equations with Caputo variable order. In order to testify the feasibility of this method, several examples are studied from the different values of parameters. In addition, the influence of the parameters of the Jacobi polynomial on the numerical results is studied. Our results reveal that the present method is effective and provide highly precise numerical solutions for solving such fractional integral differential equations.
- reproducing kernel method,
- variable fractional order,
- Jacobi polynomials,
- nonlinear integral differential equations
Citation: Zhi-Yuan Li, Mei-Chun Wang, Yu-Lan Wang. Solving a class of variable order nonlinear fractional integral differential equations by using reproducing kernel function[J]. AIMS Mathematics, 2022, 7(7): 12935-12951. doi: 10.3934/math.2022716

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Abstract

In this paper, reproducing kernel interpolation collocation method is explored for nonlinear fractional integral differential equations with Caputo variable order. In order to testify the feasibility of this method, several examples are studied from the different values of parameters. In addition, the influence of the parameters of the Jacobi polynomial on the numerical results is studied. Our results reveal that the present method is effective and provide highly precise numerical solutions for solving such fractional integral differential equations.

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