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In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the (α , β) -resolvent operator, we concern with the term u ′ (⋅) and finding a control v such that the mild solution satisfies u (b) = u b and u ′ (b) = u b ′ . Finally, we present an application to support the validity study. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of extremal mild solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach space E. By employing the method of lower and upper solutions, the measure of noncompactness, and Sadovskii's fixed point theorem, we obtain the existence of extremal mild solutions for Hilfer fractional evolution equations with noncompact semigroups. Finally, an example is provided to illustrate the feasibility of our main results. [ABSTRACT FROM AUTHOR]

We investigate the existence of mild solutions for abstract semilinear measure driven equations with nonlocal conditions. We first establish some results on Kuratowski measure of noncompactness in the space of regulated functions. Then we obtain some existence results for the abstract measure system by using the measure of noncompactness and a corresponding fixed point theorem. The usual Lipschitz-type assumptions are avoided, and the semigroup related to the linear part of the system is not claimed to be compact, which improves and generalizes some known results in the literature. [ABSTRACT FROM AUTHOR]