In this work we study the multidimensional time fractional diffusion-wave equation where the derivative in time is the fractional derivative of Caputo of order β∈ [0.2]. The introduction of fractional derivatives allows us to represent physical reality more accurately by introducing a memory mechanism in the process. These equations represent phenomena of anomalous diffusion and propagation of anomalous waves.

Applying operational techniques through Fourier and Mellin transforms, we obtain integral and serial representations of the fundamental solution for the time fractional diffusion/wave and parabolic Dirac operators in time. Several plots of the fundamental solution are presented showing the phenomenon of slow diffusion and fast diffusion according to the fractional parameter chosen.

Authors: Ferreira M, Vieira N

Published in: Journal of Mathematical Analysis and Applications