Existence and controllability of fractional evolution inclusions with impulse and sectorial operator

Year 2022, , 235 - 249, 30.09.2022

Nawal Alsarori , Kirtiwant Ghadle

https://doi.org/10.53006/rna.1018780

Abstract

Many evolutionary operations fromdiverse fields of engineering and physical sciences go through
abrupt modifications of state at specific moments of time among periods of non-stop evolution.
These operations are more conveniently modeled via impulsive differential equations and inclusions.
In this work, firstly we address the existence of mild solutions for nonlocal fractional impulsive
semilinear differential inclusions related to Caputo derivative in Banach spaces when the
linear part is sectorial. Secondly, we determine the enough, conditions for the controllability of
the studied control problem. We apply effectively fixed point theorems, contraction mapping,
multivalued analysis and fractional calculus. Moreover, we enhance our results by introducing an
illustrative examples.

Keywords

Controllability, Contraction mapping, Impulsive fractional differential inclusions, Fixed point theorem, Sectorial operators

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