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Research Article | Open Access

Non-separated inclusion problem via generalized Hilfer and Caputo operators

Laboratory of SD, Faculty of Mathematics, University of Science and Technology Houari Boumediene, P.O. Box 32, El-Alia, Bab Ezzouar, 16111, Algiers, Algeria; lachouri.adel@yahoo.fr, naasadjimi@gmail.com
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Leioa 48940, Bizkaia, Spain
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Abstract

We aimed to analyze a new class of sequential fractional differential inclusions that involves a combination of ς-Hilfer and ς-Caputo fractional derivative operators, along with non-separated boundary conditions. Two cases of convex-valued and non-convex-valued set-valued maps are considered. Our outcomes are obtained from some famous theorems of fixed point method within the framework of the set-valued analysis. Additionally, some examples are provided to illustrate the applicability of our outcomes.

Keywords

sequential inclusions problemς-Hilfer and ς-Caputo fractional derivativesexistencenonlinear analysis
CLC number: 34A08, 34A12, 34B15

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 6448-6468
DOI: 10.3934/math.2025294

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Cite this article:
Lachouri A, Adjimi N, Samei ME, et al. Non-separated inclusion problem via generalized Hilfer and Caputo operators. AIMS Mathematics, 2025, 10(3): 6448-6468. https://doi.org/10.3934/math.2025294

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Received: 08 January 2025
Revised: 12 March 2025
Accepted: 18 March 2025
Published: 15 March 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)