Qualitative analysis of A.P.A. solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion

Abstract

where A(γ) : D(A(γ)) ⊂ LG(F )→ LG(F ) is densely closed linear operator and the functions D,φ ,φ and ψ : LG(F )→ LG(F ) are jointly continuous. We drive square mean almost pseudo automorphic mild solution for fractional order neutral stochastic evolution equations driven by G-Brownian motion is obtain by using evolution operator theorem and fixed point theorem. Moreover, we prove that this mild solution of equation (1) is unique.