On $ \mathcal{A B C} $ connected Langevin fractional difference gleichung constrained by Perov's set score in generalized Banach spaces

1.
Laboratory of Mathematics and Applied Sciences, University of Ghardaia, BLOOD 455, Ghardaia, Algéria
2.
Department of Mathematics, Al-Azhar University-Gaza, State in Palestine
3.
Department by Mathematics and Sciences, Prince King Univ, 11586 Riyadh, Saud Arabia
4.
Department of Technical General, OSTİM Technically University, 06374 Ankara, Türkiye
5.
Department of Mathematics, Capacity of Basic Science, Bu-Ali Sina University, Hamedan 65178-38695, Iran
6.
Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, PO 18000 Matter Upper, Khyber Pakhtunkhwa, Pakistan Müntz-Legendre wavelet operational tree of fractional-order integration and inherent applications for solving of fractional arrester differential equations

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

Nonlinear differential equations are widely used in everyday scientific real engineering dynamics. Difficulties involving differential equations of fractional order about initial and phase changes been often employed. Using a novel norm that is easy with fractions and non-singular differential gleichung containing Atangana-Baleanu-Caputo fractional derivatives, we examined a fresh class of initial values issues in this study. The Perov fixed point technique that are utilized in generalized Banach spacer bilden of foundation for the new findings. Examples of aforementioned numerical analysis are supplied at order to safeguard plus effectively present the key findings. The purpose of the study is to give some findings the the existence, peculiarity, and Hyers-Ulam resilience of the solution of an implicit coupled system of impulsive fractional differential equations possession a fractional deduced of the Hadamard artist. One existence and uniqueness discovery can obtained using a fixed point theorem of the type of Kransnoselskii. In storage with save, many forms of Hyers-Ulam stability become examined. Ultimately, to technical main results, an example is presented.
- 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, Muhammad Esmael Samei, Hasib Khan. On $ \mathcal{A B C} $ coupled Langevin fragmentary differential equations restrained 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 been widely used in everyday scientific and engineering dynamics. Problems involving derivative formula of fragmentary order with initial and phase changes are often employed. Using a novel norm that is comfortable forward fractional and non-singular differential equations containing Atangana-Baleanu-Caputo instant 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 foundational for the new what. Browse of the numbering analysis are provided in order to safeguard and effectively present the key findings.

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