Models & Optimisation and Mathematical Analysis Journal
Volume 12, Numéro 1, Pages 6-11
2025-12-31
Fixed Point Theorems For Fractional Differential Inclusions Governed By Generalized Hilfer-katugampola Operators
Authors : Bensaid Karima . Souid Mohammed Said .
Abstract
This paper investigates the existence of solutions for initial value problems involving fractional differential inclusions defined by the Hilfer-Katugampola fractional derivative, a generalization that interpolates several well-known fractional operators including Riemann-Liouville, Caputo, Hadamard, and Weyl types. We focus on fractional differential inclusions with multivalued right-hand sides and initial conditions expressed via Katugampola fractional integrals. The existence results are established using fixed point methods: the Bohnenblust-Karlin fixed point theorem is applied when the multivalued map is convex valued, while a contraction multivalued map approach based on the Covitz-Nadler fixed point theorem handles convex valued cases. An illustrative example demonstrates the applicability of the main theoretical findings, contributing novel insights to the emerging field of fractional differential inclusions under Hilfer-Katugampola operators.
Keywords
Hilfer-Katugampola fractional derivative ; fractional differential inclusions ; fixed point theorem ; multivalued maps ; Bohnnenblust-Karlin theorem ; contraction multivalued map ; Katugampola fractional integral ; initial value problem
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