On the nonlocal hybrid $ ({\mathsf{k}}, {\rm{\mathsf{φ}}}) $-Hilfer inverse problem with delay and anticipation-Reference-Cited by-同舟云学术

On the nonlocal hybrid $ ({\mathsf{k}}, {\rm{\mathsf{φ}}}) $-Hilfer inverse problem with delay and anticipation

Published:2024 Issue:8 Volume:9 Page:22859-22882
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Salim Abdelkrim¹²,Thabet Sabri T. M.³⁴⁵,Kedim Imed⁶,Vivas-Cortez Miguel⁷

Affiliation:

1. Faculty of Technology, Hassiba Benbouali University of Chlef, P. O. Box 151, Chlef 02000, Algeria; a.salim@univ-chlef.dz

2. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P. O. Box 89, Sidi Bel-Abbes 22000, Algeria; salim.abdelkrim@yahoo.com

3. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India

4. Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen

5. Department of Mathematics, College of Science, Korea University, Seoul 02814, South Korea

6. 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

7. Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Sede Quito, Ecuador

Abstract

<p>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 $ ({\mathsf{k}}, {\rm{\mathsf{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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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