New sharp estimates of the interval length of the uniqueness results for several two-point fractional boundary value problems

Wei Zhang; Jinbo Ni; Wei Zhang; Jinbo Ni

doi:10.3934/era.2023064

Electronic Research Archive

2023, Volume 31, Issue 3: 1253-1270. doi: 10.3934/era.2023064

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New sharp estimates of the interval length of the uniqueness results for several two-point fractional boundary value problems

Wei Zhang ^,,
Jinbo Ni

School of mathematics and big data, Anhui University of Science and Technology, Huainan 232001, China

Received: 29 August 2022 Revised: 09 December 2022 Accepted: 17 December 2022 Published: 04 January 2023

This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works.
- fractional differential equation,
- two-point boundary condition,
- uniqueness of solution
Citation: Wei Zhang, Jinbo Ni. New sharp estimates of the interval length of the uniqueness results for several two-point fractional boundary value problems[J]. Electronic Research Archive, 2023, 31(3): 1253-1270. doi: 10.3934/era.2023064

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Abstract

This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works.

References

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