Hilfer fractional quantum system with Riemann-Liouville fractional derivatives and integrals in boundary conditions

Donny Passary; Sotiris K. Ntouyas; Jessada Tariboon; Donny Passary; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2024013

AIMS Mathematics

2024, Volume 9, Issue 1: 218-239. doi: 10.3934/math.2024013

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Research article

Hilfer fractional quantum system with Riemann-Liouville fractional derivatives and integrals in boundary conditions

1.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Received: 05 October 2023 Revised: 15 November 2023 Accepted: 19 November 2023 Published: 27 November 2023
MSC : 34A08, 34A12, 34B10

In this paper, we initiate the study of existence and uniqueness of solutions for a coupled system involving Hilfer fractional quantum derivatives with nonlocal boundary value conditions containing $ q $-Riemann-Liouville fractional derivatives and integrals. Our results are supported by some well-known fixed-point theories, including the Banach contraction mapping principle, Leray-Schauder alternative and the Krasnosel'skiǐ fixed-point theorem. Examples of these systems are also given in the end.
- quantum calculus,
- Hilfer derivative,
- systems,
- existence and uniqueness
Citation: Donny Passary, Sotiris K. Ntouyas, Jessada Tariboon. Hilfer fractional quantum system with Riemann-Liouville fractional derivatives and integrals in boundary conditions[J]. AIMS Mathematics, 2024, 9(1): 218-239. doi: 10.3934/math.2024013

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Abstract

In this paper, we initiate the study of existence and uniqueness of solutions for a coupled system involving Hilfer fractional quantum derivatives with nonlocal boundary value conditions containing $ q $-Riemann-Liouville fractional derivatives and integrals. Our results are supported by some well-known fixed-point theories, including the Banach contraction mapping principle, Leray-Schauder alternative and the Krasnosel'skiǐ fixed-point theorem. Examples of these systems are also given in the end.

References

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