Effects of fractional derivative and Wiener process on approximate boundary controllability of differential inclusion

One of the core concepts of contemporary control theory is the idea that a dynamical system can be controlled. Several abstract settings have been developed to describe the distributed control systems in a domain in which the control is acted through the boundary. In this manuscript, we investigate the boundary approximate controllability (ABC) of stochastic differential inclusion (SDI) with Hilfer fractional derivative (HFD) and nonlocal condition by implementing the principle of stochastic analysis, the fixed-point theorem, fractional calculus and multi-valued map. Moreover, an example is offered to define the primary results.