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Research Article | Open Access

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

Donny Passary1( ), Sotiris K. Ntouyas2, Jessada Tariboon1
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
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
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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.

Keywords

quantum calculusHilfer derivativesystemsexistence and uniqueness
CLC number: 34A08, 34A12, 34B10

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 218-239
DOI: 10.3934/math.2024013

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Cite this article:
Passary D, Ntouyas SK, Tariboon J. Hilfer fractional quantum system with Riemann-Liouville fractional derivatives and integrals in boundary conditions. AIMS Mathematics, 2024, 9(1): 218-239. https://doi.org/10.3934/math.2024013

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Received: 05 October 2023
Revised: 15 November 2023
Accepted: 19 November 2023
Published: 15 January 2024
©2024 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)