On $ \mathcal{A B C} $ coupled Langevin fractional differential equations constrained by Perov's fixed point in generalized Banach spaces

Abdelatif Boutiara; Mohammed M. Matar; Jehad Alzabut; Mohammad Esmael Samei; Hasib Khan; Abdelatif Boutiara; Mohammed M. Matar; Jehad Alzabut; Mohammad Esmael Samei; Hasib Khan

doi:10.3934/math.2023610

AIMS Mathematics

2023, Volume 8, Issue 5: 12109-12132. doi: 10.3934/math.2023610

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On $ \mathcal{A B C} $ coupled Langevin fractional differential equations constrained by Perov's fixed point in generalized Banach spaces

1.
Laboratory of Mathematics and Applied Sciences, University of Ghardaia, BP 455, Ghardaia, Algéria
2.
Department of Mathematics, Al-Azhar University-Gaza, State of Palestine
3.
Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
4.
Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Türkiye
5.
Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178-38695, Iran
6.
Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, PO 18000 Dir Upper, Khyber Pakhtunkhwa, Pakistan

Received: 30 December 2022 Revised: 06 February 2023 Accepted: 15 February 2023 Published: 21 March 2023
MSC : 34A08, 49J15, 65P99

Nonlinear differential equations are widely used in everyday scientific and engineering dynamics. Problems involving differential equations of fractional order with initial and phase changes are often employed. Using a novel norm that is comfortable for fractional and non-singular differential equations containing Atangana-Baleanu-Caputo fractional derivatives, we examined a new class of initial values issues in this study. The Perov fixed point theorems that are utilized in generalized Banach spaces form the foundation for the new findings. Examples of the numerical analysis are provided in order to safeguard and effectively present the key findings.
- coupled system,
- existence and uniqueness,
- Perov's fixed point theorem,
- $ \mathcal{A B C} $-fractional operator,
- generalized Banach space
Citation: Abdelatif Boutiara, Mohammed M. Matar, Jehad Alzabut, Mohammad Esmael Samei, Hasib Khan. On $ \mathcal{A B C} $ coupled Langevin fractional differential equations constrained by Perov's fixed point in generalized Banach spaces[J]. AIMS Mathematics, 2023, 8(5): 12109-12132. doi: 10.3934/math.2023610

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Abstract

Nonlinear differential equations are widely used in everyday scientific and engineering dynamics. Problems involving differential equations of fractional order with initial and phase changes are often employed. Using a novel norm that is comfortable for fractional and non-singular differential equations containing Atangana-Baleanu-Caputo fractional derivatives, we examined a new class of initial values issues in this study. The Perov fixed point theorems that are utilized in generalized Banach spaces form the foundation for the new findings. Examples of the numerical analysis are provided in order to safeguard and effectively present the key findings.

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