Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces

JinRong Wang, Yong Zhou, Wei Wei

Abstract


In this paper, a class of impulsive fractional evolution equations
and optimal controls in infinite dimensional spaces is considered.
A suitable concept of a $PC$-mild solution is introduced and
a suitable operator mapping is also constructed. By using a $PC$-type
Ascoli-Arzela theorem, the compactness of the operator mapping is
proven. Applying a generalized Gronwall inequality and
Leray-Schauder fixed point theorem, the existence and uniqueness of
the $PC$-mild solutions is obtained. Existence of optimal pairs for
system governed by impulsive fractional evolution equations is also
presented. Finally, an example illustrates the applicability of our
results.

Keywords


Impulsive fractional evolution equations; $PC$-mild solutions; compactness; existence; continuous dependence; optimal controls

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