Controllability Problems For Fractional Neutral Evolution Equations

The theory of fractional order calculus places an important guiding role in numerous ?elds. Although some nice results have been investigated, there still exists some ?elds that haven’t been researched.This paper mainly discusses mild solutions and controllability results for a class of fractional neutral evolution equations with Caputo derivative. Firstly, we deduce the de?nition and expression of mild solutions by using the Laplace transform and probability density. Secondly, various criteria on existence of mild solutions are obtained without compactness condition. In this paper, we have taken advantage of fractional power of operators and Hausdor? measure of non-compactness method,together with ?xed point theorem. At last, the article gives some su?cient conditions for the controllability of fractional neutral evolution equations. The results here are improvement and generalization of the exist results.