A note on approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay

In this study, we establish the approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay. The main result of this article is proven by applying some ideas of semigroup theory with fractional order and Dhage's fixed point theorem. Firstly, we prove the approximate controllability of the Hilfer fractional system. Next, we extend our study to the system with nonlocal conditions. Finally, theoretical and practical applications are presented to assist in the effectiveness of our discussion.

Automated summary

This study establishes the approximate controllability of the Hilfer fractional neutral differential inclusions with infinite delay by applying ideas of semigroup theory with fractional order and Dhage's fixed point theorem. The main result proves the approximate controllability of the Hilfer fractional system and extends the study to systems with nonlocal conditions. Theoretical and practical applications are presented to support the effectiveness of the discussion.