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Research Article | Open Access

A novel numerical method for solving the Caputo-Fabrizio fractional differential equation

Sadia Arshad1, Iram Saleem1, Ali Akgül2,3,4( ), Jianfei Huang5, Yifa Tang6, Sayed M Eldin7
COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10, Turkey
College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Center of Research, Faculty of Engineering Future University in Egypt New Cairo 11835, Egypt
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Abstract

In this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's 1 / 3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.

Keywords

fractional differential equationnon-singular operatornumerical approximationstability analysisconvergence analysis
CLC number: 26A33, 26C10

References

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9535-9556
DOI: 10.3934/math.2023481

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Cite this article:
Arshad S, Saleem I, Akgül A, et al. A novel numerical method for solving the Caputo-Fabrizio fractional differential equation. AIMS Mathematics, 2023, 8(4): 9535-9556. https://doi.org/10.3934/math.2023481

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Received: 23 September 2022
Revised: 03 January 2023
Accepted: 09 January 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)