Existence of solutions for a fractional evolution pantograph problem with a non-dense domain in a Banach space

Abstract

In the present paper, we conduct a novel study of evolution-pantograph problems involving Caputo fractional derivatives of arbitrary order ? ? (0,1) with a non-dense domain. The main objective is to establish the existence and uniqueness of mild solutions to nonlinear fractional-order evolution-pantograph equations. To this end, we employ the Laplace transform, Darbo-Sadovskii’s fixed-point theorem, and the Hausdorff measure of noncompactness as fundamental tools to prove our main results. Furthermore, an illustrative example is provided to demonstrate the practical applicability of the theoretical developments. This study makes a meaningful contribution to the field and paves the way for future research in this direction.