Dispersion relations for the time-fractional Cattaneo-Maxwell heat equation

Abstract

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations. Consequently, we provide a complete characterization of the group and phase velocities for these two cases, together with some non-trivial remarks on the nature of wave dispersion in fractional models.

18 pages, 7 figures

Cited by in corpus (3)

• The generalized Cattaneo (telegrapher's) equation and corresponding random walks
• Integral decomposition for the solutions of the generalized Cattaneo equation
• Probability distributions for the run-and-tumble models with variable speed and tumbling rate