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Research Article | Open Access

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

Rizwan Rizwan1( ), Jung Rye Lee2, Choonkil Park3( ), Akbar Zada4
Department of Mathematics, University of Buner, Buner, Pakistan
Department of Data Science, Daejin University, Kyunggi 11159, Korea
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
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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.

Keywords

Langevin equationHilfer fractional derivativeimpulseUlam-Hyers stability
CLC number: 26A33, 34A08, 34B27

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6204-6217
DOI: 10.3934/math.2022345

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Cite this article:
Rizwan R, Lee JR, Park C, et al. Qualitative analysis of nonlinear impulse langevin equation with helfer fractional order derivatives. AIMS Mathematics, 2022, 7(4): 6204-6217. https://doi.org/10.3934/math.2022345

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Received: 24 August 2021
Revised: 12 January 2022
Accepted: 12 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)