APPROXIMATE CONTROLLABILITY OF NEUTRAL DELAY INTEGRO-DIFFERENTIAL INCLUSION OF ORDER α ∈ (1,2) WITH NON-INSTANTANEOUS IMPULSES

This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the alpha-resolvent operator. Finally, the proposed results are illustrated with the help of an example.

Automated summary

This paper establishes the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay, providing sufficient conditions for the proposed control problem. The study utilizes tools such as the fixed point theorem for discontinuous multi-valued operators and the alpha-resolvent operator. The proposed results are finally demonstrated through an example.