Approximate controllability of Sobolev-type nonlocal Hilfer fractional stochastic differential system (Q2700192)

Summary: This manuscript is concerned with the approximate controllability of Sobolev-type nonlocal Hilfer fractional stochastic differential equation (FSDE) driven by the Rosenblatt process. By utilising the concepts of fractional calculus, stochastic theory, and semi-group theory, the required conditions for approximate controllability by assuming that the corresponding linear system is approximately controllable have been proved. Further, an example is provided to express the obtained theoretical result.