Fractional Diffusive Waves in the Cauchy and Signalling Problems

This work deals with the results and the simulations obtained for the time-fractional diffusion-wave equation, i.e. a diffusion-like linear integro partial differential equation containing a pseudo-differential operator interpreted as a fractional derivative in time. The data function (initial signal) is provided by a box-function and the solutions are so obtained by a convolution of the Green function with the initial data function. The relevance of the topic lies in the possibility of describing physical processes that interpolates between the different responses of the diffusion and waves equations, equipped with a physically realistic initial signal. Here two problems are considered where the use of the Laplace transform in the analysis of the problems has lead since 1990s to special functions of the Wright type.