New results concerning to approximate controllability of Hilfer fractional neutral stochastic delay integro-differential systems

This manuscript is mainly focusing on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equation with infinite delay. We study our primary outcomes by utilizing the theoretical concepts related to the fractional calculus and Krasnoselskii's fixed point theorem. First, we prove the approximate controllability of the fractional evolution system. Then, we extend our results to the concept of nonlocal conditions. Last, we provide a theoretical application to assist in the effectiveness of the discussion.

Automated summary

This manuscript mainly focuses on the approximate controllability of Hilfer fractional neutral stochastic integro-differential equation with infinite delay. The authors utilize theoretical concepts related to fractional calculus and Krasnoselskii's fixed point theorem to prove the controllability of the system and extend the results to nonlocal conditions, providing a theoretical application to support the effectiveness of the discussion.