Existence and Uniqueness of Mild Solution Where α ∈ (1,2) for Fuzzy Fractional Evolution Equations with Uncertainty

Abstract

This paper concerns with the existence and uniqueness of fuzzy fractional evolution equation with uncertainty involves function of form cDαx(t)=f(t,x(t),Dβx(t)),Iαx(0)=x0,x′(0)=x1, where 1<α<2,0<β<1. After determining the equivalent integral form of solution we establish existence and uniqueness by using Rogers conditions, Kooi type conditions and Krasnoselskii-Krein type conditions. In addition, various numerical solutions have been presented to ensure that the main result is true and effective. Finally, a few examples which express fuzzy fractional evolution equations are shown.