Fuzzy fractional neutral equation

Abstract

This paper is devoted to a class of nonlinear fuzzy neutral functional differential equations. Specifically, existence and uniqueness of fuzzy solution for the nonlinear fuzzy neutral functional differential equation\begin{equation*} {}_{gH}D^{\gamma}[x(t)-gf(t,\ x_{t})]=Ax(t)+g(t,\ x_{t}). \end{equation*} where $A$ is an operator from $E^{1}$ into itself, $\gamma\in(0,1)$ and $f$ and $g$ are continuous functions, are established via Banach fixed-point analysis approach and using the fuzzy number whose values are normal, convex upper semicontinuous, and compactly supported interval in $E^{1}$.