Total controllability of neutral fractional differential equation with non-instantaneous impulsive effects

Abstract

In this article, we establish some sufficient conditions for total controllability of a neutral fractional differential system with impulsive conditions in the finite-dimensional spaces. This type of controllability concerns the controllability problem not only at the final time but also at the impulse time. We use Mittag-Leffler matrix function, nonlinear functional analysis, controllability Grammian type matrices and fixed point theorem due to Krasnoselskii’s to establish these results. Also, we extend these results for the studied problem with the integro term. At last, some simulated examples are given to validate the obtained results.