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.

In this manuscript, the notion of a hesitant fuzzy soft fixed point is introduced. Using this notion and the concept of Suzuki-type ( $\mu ,\nu$)-weak contraction for hesitant fuzzy soft set valued-mapping, some fixed point results are established in the framework of metric spaces. Based on the presented work, some examples reflecting decision-making problems related to real life are also solved. The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty, such as choosing the best options in multi-criteria settings. We noted that the presented work combines and generalizes two major concepts, the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.