Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation

36Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

In this paper, the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order α, 1 ≤ α ≤ 2 and with constant coefficients is revisited. It is known that the diffusion and the wave equations behave quite differently regarding their response to a localized disturbance. Whereas the diffusion equation describes a process where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates between these two different responses and investigate the behavior of its fundamental solution for the signalling problem in detail. In particular, the maximum location, the maximum value, and the propagation velocity of the maximum point of the fundamental solution for the signalling problem are described analytically and calculated numerically. © 2013 Versita Warsaw and Springer-Verlag Wien.

Cite

CITATION STYLE

APA

Luchko, Y., & Mainardi, F. (2013). Some properties of the fundamental solution to the signalling problem for the fractional diffusion-wave equation. Central European Journal of Physics, 11(6), 666–675. https://doi.org/10.2478/s11534-013-0247-8

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free