Coupled Hybrid Proportional Fractional Systems of Caputo-Type in Generalized Banach Spaces

Yasir A. Madani; Oualid Zentar; Sidi Mohammed Benhabi; Tayeb Mahrouz; Abdelkader Moumen

doi:10.37256/cm.7220268130

Authors

Yasir A. Madani Department of Mathematics, College of Science, University of Hail, Hail, 55473, Saudi Arabia
Oualid Zentar Department of Computer Science and Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Tiaret, P.O. Box 78, Algeria
Sidi Mohammed Benhabi Department of Computer Science and Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Tiaret, P.O. Box 78, Algeria
Tayeb Mahrouz Department of Computer Science and Laboratory of Research in Artificial Intelligence and Systems (LRAIS), University of Tiaret, Tiaret, P.O. Box 78, Algeria
Abdelkader Moumen Department of Mathematics, College of Science, University of Hail, Hail, 55473, Saudi Arabia https://orcid.org/0000-0003-1080-3686

DOI:

https://doi.org/10.37256/cm.7220268130

Keywords:

hybrid proportional-Caputo derivative, coupled system, generalized Banach space

Abstract

This paper presents new quantitative results for a class of coupled systems involving the hybrid proportional-Caputo fractional derivative. First, a variant of Perov's fixed point theorem, combined with the Bielecki norm, is employed to establish existence and uniqueness. Second, an additional existence result is derived using Krasnosel'skii's fixed point theorem within the framework of generalized Banach spaces. Finally, Urs's approach is employed to analyze the Hyers-Ulam stability of solutions to the proposed problem. To validate the theoretical results, several illustrative examples are presented.

Coupled Hybrid Proportional Fractional Systems of Caputo-Type in Generalized Banach Spaces

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