Existence and stability analysis for a coupled system of $ \mathtt{q} $-fractional implicit jerk Caputo derivatives with $ \mathtt{q} $-Erdélyi-Kober fractional integral conditions

Jiafa Xu; Yujun Cui; Khansa Hina Khalid; Akbar Zada; Ioan-Lucian Popa; Afef Kallekh; Jiafa Xu; Yujun Cui; Khansa Hina Khalid; Akbar Zada; Ioan-Lucian Popa; Afef Kallekh

doi:10.3934/mmc.2025018

Mathematical Modelling and Control

2025, Volume 5, Issue 3: 258-279. doi: 10.3934/mmc.2025018

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Research article

Existence and stability analysis for a coupled system of $ \mathtt{q} $-fractional implicit jerk Caputo derivatives with $ \mathtt{q} $-Erdélyi-Kober fractional integral conditions

1.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
2.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
3.
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
4.
Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, Alba Iulia, 510009, Romania
5.
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
6.
Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia

Received: 06 August 2024 Revised: 27 November 2024 Accepted: 29 December 2024 Published: 21 July 2025

This manuscript demonstrates the existence, uniqueness, and different kinds of Ulam stability for a $ \mathtt{q} $-Caputo implicit fractional jerk coupled system involving $ \mathtt{q} $-fractional Erdélyi-Kober integral conditions. The existence and uniqueness results were investigated by employing the Leray-Schauder alternative and the Banach contraction mapping principle. We also derived various kinds of Ulam stability under specific conditions. We provided an example to verify our main results.
- coupled system,
- fractional jerk equation,
- Erdélyi-Kober $ \mathtt{q} $-fractional integral conditions,
- fixed point theorem,
- Ulam-Hyers stability
Citation: Jiafa Xu, Yujun Cui, Khansa Hina Khalid, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh. Existence and stability analysis for a coupled system of $ \mathtt{q} $-fractional implicit jerk Caputo derivatives with $ \mathtt{q} $-Erdélyi-Kober fractional integral conditions[J]. Mathematical Modelling and Control, 2025, 5(3): 258-279. doi: 10.3934/mmc.2025018

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Abstract

This manuscript demonstrates the existence, uniqueness, and different kinds of Ulam stability for a $ \mathtt{q} $-Caputo implicit fractional jerk coupled system involving $ \mathtt{q} $-fractional Erdélyi-Kober integral conditions. The existence and uniqueness results were investigated by employing the Leray-Schauder alternative and the Banach contraction mapping principle. We also derived various kinds of Ulam stability under specific conditions. We provided an example to verify our main results.

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