Controllability of fractional differential evolution equation of order $ \gamma \in (1, 2) $ with nonlocal conditions

Abstract

<abstract><p>This paper investigates the existence of positive mild solutions and controllability for fractional differential evolution equations of order $ \gamma \in (1, 2) $ with nonlocal conditions in Banach spaces. Our approach is based on Schauder's fixed point theorem, Krasnoselskii's fixed point theorem, and the Arzelà-Ascoli theorem. Finally, we include an example to verify our theoretical results.</p></abstract>