Controllability of Hilfer type fractional evolution neutral integro-differential inclusions with non-instantaneous impulses

Abstract

<p style='text-indent:20px;'>In this manuscript the controllability of Hilfer fractional neutral differential inclusions with non-instantaneous impulse in Banach space is investigated by using semi-group theory, fractional calculus, upper semi-continuous (u.s.c), multi-functions and Mönch fixed point theorem. Sufficient conditions are derived by using Hausdorff measure of non-compactness (MNC). Further, the obtained result is illustrated by an example.</p>

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

“…A dynamical system is said to be controllable if it can be guided, by the set of admissible inputs, from an arbitrary initial state to an arbitrary final state. Several writers have explored controllability difficulties for various types of dynamical systems (see [18][19][20][21][22][23]) and the references therein. The researcher Wang et al [24] established the controllability of Hilfer fractional NII semilinear differential inclusions with nonlocal conditions.…”

“…In 2016, Gautam and Dabas [32] established mild solutions for a class of neutral fractional functional differential equations with NII. Nowadays, most researchers [18,21,24,30,[33][34][35][36] study non-instantaneous impulses with the HFD. Researchers delve into the study of non-densely defined operators to tackle the complexities of control and ensure the efficient operation of a wide range of systems, from robotics and autonomous vehicles to power grids and biological networks [9,10,14,19,22,25].…”