Optimal and total controllability approach of non-instantaneous Hilfer fractional derivative with integral boundary condition

PLoS One. 2024 Feb 28;19(2):e0297478. doi: 10.1371/journal.pone.0297478. eCollection 2024.

Abstract

The focus of this work is on the absolute controllability of Hilfer impulsive non-instantaneous neutral derivative (HINND) with integral boundary condition of any order. Total controllability refers to the system's ability to be controlled during the impulse time. Kuratowski measure and semigroup theory in Banach space yield the results. Furthermore, we talked about optimal controllability in conjunction with appropriate limitations. Our established outcomes are described using an example.

Grants and funding

The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2023/01/2189822).