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Research Article | Open Access

Separated boundary value problems via quantum Hilfer and Caputo operators

Idris Ahmed1,2, Sotiris K. Ntouyas3, 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, Faculty of Natural and Applied Sciences, Sule Lamido University, P.M.B 048 Kafin-Hausa, Jigawa State, Nigeria
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
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Abstract

This paper describes a new class of boundary value fractional-order differential equations of the q-Hilfer and q-Caputo types, with separated boundary conditions. The presented problem is converted to an equivalent integral form, and fixed-point theorems are used to prove the existence and uniqueness of solutions. Moreover, several special cases demonstrate how the proposed problems advance beyond the existing literature. Examples are provided to support the analysis presented.

Keywords

Hilfer fractional derivativeCaputo derivativeseparated boundary conditionexistencefixed point theorems
CLC number: 26A33, 34A12, 34A34, 34D20

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 19473-19494
DOI: 10.3934/math.2024949

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Cite this article:
Ahmed I, Ntouyas SK, Tariboon J. Separated boundary value problems via quantum Hilfer and Caputo operators. AIMS Mathematics, 2024, 9(7): 19473-19494. https://doi.org/10.3934/math.2024949

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Received: 01 May 2024
Revised: 27 May 2024
Accepted: 07 June 2024
Published: 15 July 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)