A study of Wiener-Hopf dynamical systems for variational inequalities in the setting of fractional calculus

Kamsing Nonlaopon; Awais Gul Khan; Muhammad Aslam Noor; Muhammad Uzair Awan; Kamsing Nonlaopon; Awais Gul Khan; Muhammad Aslam Noor; Muhammad Uzair Awan

doi:10.3934/math.2023139

AIMS Mathematics

2023, Volume 8, Issue 2: 2659-2672. doi: 10.3934/math.2023139

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Research article

A study of Wiener-Hopf dynamical systems for variational inequalities in the setting of fractional calculus

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematics, Government College University, Allama Iqbal Road, Faisalabad, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad, Islamabad, Pakistan

Received: 02 August 2022 Revised: 27 September 2022 Accepted: 13 October 2022 Published: 08 November 2022
MSC : 49J40, 46T99, 47H05

In this paper, we consider a new fractional dynamical system for variational inequalities using the Wiener Hopf equations technique. We show that the fractional Wiener-Hopf dynamical system is exponentially stable and converges to its unique equilibrium point under some suitable conditions. We also discuss some special cases, which can be obtained from our main results.
- dynamical systems,
- fractional derivative,
- convergence,
- variational inequalities
Citation: Kamsing Nonlaopon, Awais Gul Khan, Muhammad Aslam Noor, Muhammad Uzair Awan. A study of Wiener-Hopf dynamical systems for variational inequalities in the setting of fractional calculus[J]. AIMS Mathematics, 2023, 8(2): 2659-2672. doi: 10.3934/math.2023139

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Abstract

In this paper, we consider a new fractional dynamical system for variational inequalities using the Wiener Hopf equations technique. We show that the fractional Wiener-Hopf dynamical system is exponentially stable and converges to its unique equilibrium point under some suitable conditions. We also discuss some special cases, which can be obtained from our main results.

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