Null controllability of Hilfer fractional stochastic differential equations with nonlocal conditions

This paper assesses a class of nonlocal Hilfer fractional stochastic differential equations (NHFSDEs) governed by fractional Brownian motion (fBm). New sufficient condition of exact null controllability for this stochastic setting has been investigated using fractional calculus, fixed point theory and a theory of resolvent operator. The derived result is new because it generalizes several of previously published results. However, the obtained results are proven by an illustration using stochastic partial differential equations to demonstrate the present application characteristic of null controllability. A filter example is demonstrated to make use of resolvent operator in a practical way.