Non-separated inclusion problem via generalized Hilfer and Caputo operators

Adel Lachouri; Naas Adjimi; Mohammad Esmael Samei; Manuel De la Sen; Adel Lachouri; Naas Adjimi; Mohammad Esmael Samei; Manuel De la Sen

doi:10.3934/math.2025294

AIMS Mathematics

2025, Volume 10, Issue 3: 6448-6468. doi: 10.3934/math.2025294

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Non-separated inclusion problem via generalized Hilfer and Caputo operators

1.
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
2.
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
3.
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

Received: 08 January 2025 Revised: 12 March 2025 Accepted: 18 March 2025 Published: 21 March 2025
MSC : 34A08, 34A12, 34B15

We aimed to analyze a new class of sequential fractional differential inclusions that involves a combination of $ \varsigma $-Hilfer and $ \varsigma $-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.
- sequential inclusions problem,
- $ \varsigma $-Hilfer and $ \varsigma $-Caputo fractional derivatives,
- existence,
- nonlinear analysis
Citation: Adel Lachouri, Naas Adjimi, Mohammad Esmael Samei, Manuel De la Sen. Non-separated inclusion problem via generalized Hilfer and Caputo operators[J]. AIMS Mathematics, 2025, 10(3): 6448-6468. doi: 10.3934/math.2025294

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Abstract

We aimed to analyze a new class of sequential fractional differential inclusions that involves a combination of $ \varsigma $-Hilfer and $ \varsigma $-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.

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