New fractional results for Langevin equations through extensive fractional operators

Mohamed A. Barakat; Abd-Allah Hyder; Doaa Rizk; Mohamed A. Barakat; Abd-Allah Hyder; Doaa Rizk

doi:10.3934/math.2023309

AIMS Mathematics

2023, Volume 8, Issue 3: 6119-6135. doi: 10.3934/math.2023309

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Research article

New fractional results for Langevin equations through extensive fractional operators

1.
Department of Computer Science, College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
3.
Department of Mathematics, College of Science, King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia
4.
Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt
5.
Department of Mathematics, College of Science and Arts, Qassim University, Al-Asyah, Saudi Arabia

Received: 17 October 2022 Revised: 22 December 2022 Accepted: 23 December 2022 Published: 29 December 2022
MSC : 26A33, 34A08, 45M10

Fractional Langevin equations play an important role in describing a wide range of physical processes. For instance, they have been used to describe single-file predominance and the behavior of unshackled particles propelled by internal sounds. This article investigates fractional Langevin equations incorporating recent extensive fractional operators of different orders. Nonperiodic and nonlocal integral boundary conditions are assumed for the model. The Hyres-Ulam stability, existence, and uniqueness of the solution are defined and analyzed for the suggested equations. Also, we utilize Banach contraction principle and Krasnoselskii fixed point theorem to accomplish our results. Moreover, it will be apparent that the findings of this study include various previously obtained results as exceptional cases.
- extensive fractional integral operator,
- fixed point theorems,
- fractional Langevin equation,
- Hyres-Ulam stability,
- nonlocal conditions
Citation: Mohamed A. Barakat, Abd-Allah Hyder, Doaa Rizk. New fractional results for Langevin equations through extensive fractional operators[J]. AIMS Mathematics, 2023, 8(3): 6119-6135. doi: 10.3934/math.2023309

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Abstract

Fractional Langevin equations play an important role in describing a wide range of physical processes. For instance, they have been used to describe single-file predominance and the behavior of unshackled particles propelled by internal sounds. This article investigates fractional Langevin equations incorporating recent extensive fractional operators of different orders. Nonperiodic and nonlocal integral boundary conditions are assumed for the model. The Hyres-Ulam stability, existence, and uniqueness of the solution are defined and analyzed for the suggested equations. Also, we utilize Banach contraction principle and Krasnoselskii fixed point theorem to accomplish our results. Moreover, it will be apparent that the findings of this study include various previously obtained results as exceptional cases.

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