Uniqueness criteria for initial value problem of conformable fractional differential equation

Yumei Zou; Yujun Cui; Yumei Zou; Yujun Cui

doi:10.3934/era.2023207

Electronic Research Archive

2023, Volume 31, Issue 7: 4077-4087. doi: 10.3934/era.2023207

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Uniqueness criteria for initial value problem of conformable fractional differential equation

Yumei Zou ,
Yujun Cui ^,

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received: 26 April 2023 Revised: 19 May 2023 Accepted: 23 May 2023 Published: 26 May 2023

This paper presents four uniqueness criteria for the initial value problem of a differential equation which depends on conformable fractional derivative. Among them is the generalization of Nagumo-type uniqueness theory and Lipschitz conditional theory, and advances its development in proving fractional differential equations. Finally, we verify the main conclusions of this paper by providing four concrete examples.
- conformable fractional differential equations,
- uniqueness of solution,
- initial value problem
Citation: Yumei Zou, Yujun Cui. Uniqueness criteria for initial value problem of conformable fractional differential equation[J]. Electronic Research Archive, 2023, 31(7): 4077-4087. doi: 10.3934/era.2023207

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Abstract

This paper presents four uniqueness criteria for the initial value problem of a differential equation which depends on conformable fractional derivative. Among them is the generalization of Nagumo-type uniqueness theory and Lipschitz conditional theory, and advances its development in proving fractional differential equations. Finally, we verify the main conclusions of this paper by providing four concrete examples.

References

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