  In this paper we investigate fractional differential equations with Hilfer
fractional derivative of order $1<\gamma<2$ and type $\delta \in [0,1]$ in a
Banach space. We introduce a family of general fractional cosine operator
functions of order $1<\gamma<2$ and type $\delta \in [0,1]$ and discuss their
properties to give a suitable definition of mild solution of a semilinear
evolution equation. In last section an example is presented.
