Qualitative analysis of nonlinear impulse langevin equation with helfer fractional order derivatives

Rizwan Rizwan; Jung Rye Lee; Choonkil Park; Akbar Zada; Rizwan Rizwan; Jung Rye Lee; Choonkil Park; Akbar Zada

doi:10.3934/math.2022345

AIMS Mathematics

2022, Volume 7, Issue 4: 6204-6217. doi: 10.3934/math.2022345

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Research article

Qualitative analysis of nonlinear impulse langevin equation with helfer fractional order derivatives

1.
Department of Mathematics, University of Buner, Buner, Pakistan
2.
Department of Data Science, Daejin University, Kyunggi 11159, Korea
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
4.
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Received: 24 August 2021 Revised: 12 January 2022 Accepted: 12 January 2022 Published: 18 January 2022
MSC : 26A33, 34A08, 34B27

In this manuscript, a class of impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness and different types of Ulam-Hyers stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results.
- Langevin equation,
- Hilfer fractional derivative,
- impulse,
- Ulam-Hyers stability
Citation: Rizwan Rizwan, Jung Rye Lee, Choonkil Park, Akbar Zada. Qualitative analysis of nonlinear impulse langevin equation with helfer fractional order derivatives[J]. AIMS Mathematics, 2022, 7(4): 6204-6217. doi: 10.3934/math.2022345

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Abstract

In this manuscript, a class of impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness and different types of Ulam-Hyers stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results.

References

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