Controllability For Fractional Neutral Evolution Equations With Hilfer Derivative

This paper is mainly discussed a class of fractional neutral evolution equations with Hilfer derivative. Fractional equations with Hilfer derivative includes fractional equations with Riemann-Liouville derivative and fractional equations with Caputo derivative. Firstly, taking the Laplace transform, we deduce the definition and ex-pression of mild solutions. Secondly, by using fractional power of operators and nonlinear functional analysis method together with Krasnoselskii fixed point theo-rem, various criteria on existence of mild solutions are obtained. At last, we discusses the controllability of fractional neutral evolution equations with Hilfer derivative.The results of this paper extend some known.