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In this paper we investigate fractional differential equations with Hilferfractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in aBanach space. We introduce a family of general fractional cosine operatorfunctions of order $1<\gamma<2$ and type $\delta \in [0,1]$ and discuss theirproperties to give a suitable definition of mild solution of a semilinearevolution equation. In last section an example is presented.

Study of fractional evolution equations involving Hilfer fractional derivative of order $1<\gamma<2$ and type $0 \leq \delta \leq 1$