Measure of noncompactness approach to nonlinear fractional pantograph differential equations

A. El Mfadel^ab, S. Melliani<sup>a

a</sup> Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
^b Higher School of Technology, Sultan Moulay Slimane University, Khenifra, Morocco

Abstract: The aim of this manuscript is to explore the existence and uniqueness of solutions for a class of nonlinear $\Psi$-Caputo fractional pantograph differential equations subject to nonlocal conditions. The proofs rely on key results in topological degree theory for condensing maps, coupled with the method of measures of noncompactness and essential tools in $\Psi$-fractional calculus. To support the theoretical ndings, a nontrivial example is presented as an application.

Keywords and phrases: $\Psi$-fractional integral, $\Psi$-Caputo fractional derivative, topological degree theory.

MSC: 26A33, 34A08, 47H08

Received: 20.12.2023

Language: English

DOI: 10.32523/2077-9879-2025-16-1-49-59