Approximate Controllability of Fractional Evolution System on Non-Dense Domain

Abstract

This article explores the existence and approximate controllability of integral solutions for Hilfer fractional evolution equations in a non-dense domain. Leveraging the well-known generalized Banach contraction theorem, we establish both the existence and uniqueness of the integral solution. Furthermore, we adopt a sequential approach to derive results related to approximate controllability, without relying on the compactness of semigroups or the uniform boundedness of nonlinear functions. To validate our findings, we present and discuss an illustrative example.