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

Sadia Arshad; Iram Saleem; Ali Akgül; Jianfei Huang; Yifa Tang; Sayed M Eldin; Sadia Arshad; Iram Saleem; Ali Akgül; Jianfei Huang; Yifa Tang; Sayed M Eldin

doi:10.3934/math.2023481

AIMS Mathematics

2023, Volume 8, Issue 4: 9535-9556. doi: 10.3934/math.2023481

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Research article

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

1.
COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3.
Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
4.
Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10, Turkey
5.
College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
6.
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
7.
Center of Research, Faculty of Engineering Future University in Egypt New Cairo 11835, Egypt

Received: 23 September 2022 Revised: 03 January 2023 Accepted: 09 January 2023 Published: 20 February 2023
MSC : 26A33, 26C10

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.
- fractional differential equation,
- non-singular operator,
- numerical approximation,
- stability analysis,
- convergence analysis
Citation: Sadia Arshad, Iram Saleem, Ali Akgül, Jianfei Huang, Yifa Tang, Sayed M Eldin. A novel numerical method for solving the Caputo-Fabrizio fractional differential equation[J]. AIMS Mathematics, 2023, 8(4): 9535-9556. doi: 10.3934/math.2023481

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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.

References

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