Controllability of fractional stochastic evolution inclusion via Hilfer derivative of fixed point theory

In this study, we use the Hilfer derivative to analyze the approximate controllability of fractional stochastic evolution inclusions (FSEIs) with nonlocal conditions. By assuming that the corresponding linear system is approximately controllable, we obtain a novel set of adequate requirements for the approximate controllability of nonlinear FSEIs in meticulous detail. The fixed-point theorem for multi-valued operators and fractional calculus are used to achieve the results. Finally, we use several instances to demonstrate our findings.

Automated summary

In this study, the Hilfer derivative is utilized to analyze the approximate controllability of fractional stochastic evolution inclusions (FSEIs) with nonlocal conditions. By assuming that the corresponding linear system is approximately controllable, a novel set of adequate requirements for the approximate controllability of nonlinear FSEIs is obtained in meticulous detail. The results are achieved by employing the fixed-point theorem for multi-valued operators and fractional calculus. Finally, several instances are used to demonstrate the findings.