In this paper, we study the existence of integral solutions for impulsive evolution equations with nonlocal conditions where the linear part is nondensely defined. Some existence results of integral solutions to such problems are obtained under the conditions in respect of the Hausdorff's measure of noncompactness. Example is provided to illustrate the main result. c 2012 NGA. All rights reserved.

In this paper, we establish two sufficient conditions for nonlocal controllability for fractional evolution systems. Since there is no compactness of characteristic solution operators, our theorems guarantee the effectiveness of controllability results under some weakly compactness conditions.

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Of concern are the existence and approximate controllability of fractional differential equations governed by a linear closed operator which generates a resolvent. Using the analytic resolvent method and the continuity of a resolvent in the uniform operator topology, we derive the existence and approximate controllability results of a fractional control system. MSC: 34K37; 47A10; 49J15

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Under a compactness assumption on the resolvent, some properties on relevant operators generated by resolvent are given. Existence results of fractional control systems are obtained by Schauder?s fixed point theorem and approximation techniques. Furthermore, the approximately controllable result is acquired under the assumption that the corresponding linear system is approximately controllable, which improves and extends some results on this topic.