New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

Wei Zhang; Jifeng Zhang; Jinbo Ni; Wei Zhang; Jifeng Zhang; Jinbo Ni

doi:10.3934/math.2022064

AIMS Mathematics

2022, Volume 7, Issue 1: 1074-1094. doi: 10.3934/math.2022064

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Research article

New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

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

Received: 12 July 2021 Accepted: 12 October 2021 Published: 19 October 2021
MSC : 34A08, 34B05, 34B10

In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.
- Lyapunov-type inequality,
- Hilfer-Katugampola fractional derivative,
- multi-point boundary condition
Citation: Wei Zhang, Jifeng Zhang, Jinbo Ni. New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative[J]. AIMS Mathematics, 2022, 7(1): 1074-1094. doi: 10.3934/math.2022064

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Abstract

In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.

References

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