  This paper is concerned with the fractional evolution equation with a
discrete distribution of Caputo time-derivatives such that the largest and the
smallest orders, $\alpha$ and $\alpha_m$, satisfy the conditions $1<\alpha\le
2$ and $\alpha-\alpha_m\le 1$. First, based on a study of the related
propagation function, the nonnegativity of the fundamental solutions to the
spatially one-dimensional Cauchy and signaling problems is proven and
propagation speed of a disturbance is discussed. Next, we study the equation
with a general linear spatial differential operator defined in a Banach space
and suppose it generates a cosine family. A subordination principle is
established, which implies the existence of a unique solution and gives an
integral representation of the solution operator in terms of the corresponding
cosine family and a probability density function. Explicit representation of
the probability density function is derived. The subordination principle is
applied for obtaining regularity results. The analytical findings are supported
by numerical work.
