Existence and qualitative behavior of mild solutions for fuzzy boundary value problem with nonlocal conditions

Abstract

The focus of this study is on boundary-value issues for Caputo-type fractional differential equations of order $1<q<2$. To begin, we demonstrate the existence theorem of mild solutions under certain lesser constraints combining the measure of non-compactness and Darbo's fixed-point theorem. The generalised Ulam-Hyers stability requirements are then investigated. The insights provided here enlarge and enhance on several already established discoveries. subsequently an illustration is provided to demonstrate the truthfulness of what has been found.