Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation - Naveed Iqbal; Azmat Ullah Khan Niazi; Ramsha Shafqat; Shamsullah Zaland (Journal of Function Spaces)
In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form  0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.