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

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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