Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative

Zhoujin Cui; Zhoujin Cui

doi:10.3934/math.2022779

AIMS Mathematics

2022, Volume 7, Issue 8: 14139-14153. doi: 10.3934/math.2022779

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Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative

Zhoujin Cui ^{1,2
,
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1.
School of Economics and Management, Jiangsu Maritime Institute, Nanjing 211170, China
2.
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received: 31 March 2022 Revised: 20 May 2022 Accepted: 23 May 2022 Published: 27 May 2022
MSC : 26A33, 34A08

In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained. The fractional derivative concerned here is the Caputo-Fabrizio form, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. In addition, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and appropriate fractional order is very important in the modeling process.
- nonlinear differential equation,
- Caputo-Fabrizio derivative,
- nonsingular kernel,
- implicit analytical solution
Citation: Zhoujin Cui. Solutions of some typical nonlinear differential equations with Caputo-Fabrizio fractional derivative[J]. AIMS Mathematics, 2022, 7(8): 14139-14153. doi: 10.3934/math.2022779

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Abstract

In this paper, the solutions of some typical nonlinear fractional differential equations are discussed, and the implicit analytical solutions are obtained. The fractional derivative concerned here is the Caputo-Fabrizio form, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. In addition, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and appropriate fractional order is very important in the modeling process.

References

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