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Research Article | Open Access

On the nonlocal hybrid (k,φ)-Hilfer inverse problem with delay and anticipation

Faculty of Technology, Hassiba Benbouali University of Chlef, P. O. Box 151, Chlef 02000, Algeria; a.salim@univ-chlef.dz
Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P. O. Box 89, Sidi Bel-Abbes 22000, Algeria; salim.abdelkrim@yahoo.com
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen
Department of Mathematics, College of Science, Korea University, Seoul 02814, South Korea
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia; i.kedim@psau.edu.sa
Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, PontificalCatholic University of Ecuador, Sede Quito, Ecuador
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Abstract

This paper focused on establishing results regarding the existence of solutions for a class of nonlocal terminal value problems involving hybrid implicit nonlinear fractional differential equations with the (k,φ)-Hilfer fractional derivative, which includes both finite delay and anticipation arguments. Our analysis was based on the Banach fixed point technique, and the Schauder and Krasnoselskii fixed point theorems. Moreover, illustrative examples were considered to support our new results.

Keywords

(k, φ)-Hilfer fractional derivativehybrid equationsterminal value problemretarded argumentsadvanced argumentsexistenceuniquenessnonlocal condition
CLC number: 26A33, 34A08, 34A12

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22859-22882
DOI: 10.3934/math.20241112

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Cite this article:
Salim A, Thabet STM, Kedim I, et al. On the nonlocal hybrid (k,φ)-Hilfer inverse problem with delay and anticipation. AIMS Mathematics, 2024, 9(8): 22859-22882. https://doi.org/10.3934/math.20241112

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Received: 18 May 2024
Revised: 02 July 2024
Accepted: 08 July 2024
Published: 15 August 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)