The abstract Cauchy problem for the non-stationary bulk queue M(t)|M[k, B]|1 Abstract We derived state probability equations describing the queue M (t)| M [k, B]|1 and formulated as an abstract Cauchy problem to investigate by means of the semi-group theory of bounded linear operators in functional analysis. With regard to the abstract Cauchy problem of this queue, we determined the eigenfuncti...

Every infinitely divisible law defines a convolution semigroup that solves an abstract Cauchy problem. In the fractional Cauchy problem, we replace the first order time derivative by a fractional derivative. Solutions to fractional Cauchy problems are obtained by subordinating the solution to the original Cauchy problem. Fractional Cauchy problems are useful in physics to model anomalous diffus...