Switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives

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

doi:10.3934/math.2021757

AIMS Mathematics

2021, Volume 6, Issue 12: 13092-13118. doi: 10.3934/math.2021757

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Research article

Switched coupled system of nonlinear impulsive Langevin equations with mixed 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: 18 May 2021 Accepted: 05 September 2021 Published: 14 September 2021
MSC : 26A33, 34A08, 34B27

In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.
- Langevin equation,
- Caputo derivative,
- impulse,
- Ulam-Hyers-Rassias stability
Citation: Rizwan Rizwan, Jung Rye Lee, Choonkil Park, Akbar Zada. Switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives[J]. AIMS Mathematics, 2021, 6(12): 13092-13118. doi: 10.3934/math.2021757

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Abstract

In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.

References

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