Evolution of the initial box-signal for time-fractional diffusion–wave equation in a case of different spatial dimensions

In the case of time-fractional diffusion–wave equation considered in the spatial domain −∞<x<∞, evolution of initial box-signal was investigated by Mainardi [F. Mainardi, Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos Solitons Fractals 7 (1996) 1461–1477]. In the present paper, we supplement Mainardi’s results with additional numerical calculations illustrating the behavior of the solution and solve the corresponding problems for axisymmetric and central symmetric cases. The obtained results show an unusual behavior of solutions.