Partial approximate controllability results for fractional order stochastic evolution equations using approximation method

Abstract

The sufficient conditions for existence and partial approximate controllability of fractional stochastic evolution equations with nonlocal initial conditions have been discussed. The discussion is based on the variational method, fractional calculus, Schauder's fixed point theorem, and stochastic analysis. Contrary to the results available in the literature, the non-local function does not need to be compact or satisfy Lipschitz's condition. Moreover, the pertinent nonlinear function does not need to be uniformly bounded. At the end, an application has also been demonstrated.