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Research Article | Open Access

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

Jiafa Xu1, Yujun Cui2( ), Khansa Hina Khalid3, Akbar Zada3, Ioan-Lucian Popa4,5, Afef Kallekh6
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
Department of Computing, Mathematics and Electronics, "1 Decembrie 1918" University of Alba Iulia, Alba Iulia, 510009, Romania
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Department of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi Arabia
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Abstract

This manuscript demonstrates the existence, uniqueness, and different kinds of Ulam stability for a q -Caputo implicit fractional jerk coupled system involving 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.

Keywords

coupled systemfractional jerk equationErdélyi-Kober q-fractional integral conditionsfixed point theoremUlam-Hyers stability

References

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Mathematical Modelling and Control
Volume 5 Issue 3,
September 2025
Pages 258-279
DOI: 10.3934/mmc.2025018

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Cite this article:
Xu J, Cui Y, Khalid KH, et al. Existence and stability analysis for a coupled system of q -fractional implicit jerk Caputo derivatives with q -Erdélyi-Kober fractional integral conditions. Mathematical Modelling and Control, 2025, 5(3): 258-279. https://doi.org/10.3934/mmc.2025018

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Received: 06 August 2024
Revised: 27 November 2024
Accepted: 29 December 2024
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)