On nonlinear fractional Hahn integrodifference equations via nonlocal fractional Hahn integral boundary conditions

Nichaphat Patanarapeelert; Jiraporn Reunsumrit; Thanin Sitthiwirattham; Nichaphat Patanarapeelert; Jiraporn Reunsumrit; Thanin Sitthiwirattham

doi:10.3934/math.20241667

AIMS Mathematics

2024, Volume 9, Issue 12: 35016-35037. doi: 10.3934/math.20241667

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Research article

On nonlinear fractional Hahn integrodifference equations via nonlocal fractional Hahn integral boundary conditions

1.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Research Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
3.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Received: 23 October 2024 Revised: 03 December 2024 Accepted: 05 December 2024 Published: 16 December 2024
MSC : 34K10, 39A10, 39A11, 39A13, 39A70

All authors Fractional Hahn differences and fractional Hahn integrals have various applications in fields where discrete fractional calculus plays a significant role, such as in discrete biological modeling and signal processing to handle systems with memory effects. In this study, the existence and uniqueness of solutions for a Riemann-Liouville fractional Hahn integrodifference equation with nonlocal fractional Hahn integral boundary conditions are investigated. To establish these results, we apply the Banach and Schauder fixed-point theorems. Furthermore, the Hyers-Ulam stability of solutions is studied.
- fractional Hahn integral,
- Riemann-Liouville fractional Hahn difference,
- boundary value problems,
- existence,
- Hyers-Ulam stability
Citation: Nichaphat Patanarapeelert, Jiraporn Reunsumrit, Thanin Sitthiwirattham. On nonlinear fractional Hahn integrodifference equations via nonlocal fractional Hahn integral boundary conditions[J]. AIMS Mathematics, 2024, 9(12): 35016-35037. doi: 10.3934/math.20241667

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Abstract

All authors Fractional Hahn differences and fractional Hahn integrals have various applications in fields where discrete fractional calculus plays a significant role, such as in discrete biological modeling and signal processing to handle systems with memory effects. In this study, the existence and uniqueness of solutions for a Riemann-Liouville fractional Hahn integrodifference equation with nonlocal fractional Hahn integral boundary conditions are investigated. To establish these results, we apply the Banach and Schauder fixed-point theorems. Furthermore, the Hyers-Ulam stability of solutions is studied.

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