Fuzzy fractional evolution equation with a non-dense domain operator

Abstract

We aim to establish the existence and uniqueness of the mild fuzzy solution to a fuzzy nonlinear fractional evolution equation.
This problem involves a non-dense domain operator and employs the fuzzy Caputo fractional derivative, denoted as \( ^C D_{0^{+},gH}^{q} \)
with order \( q \in (0,1) \), within the framework of the triangular fuzzy number space \( \Omega \).
Furthermore, we consider nonlocal conditions and provide an illustrative example to demonstrate the applicability of our findings.