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

TL;DR

This paper analyzes the dispersion relations of the classical and time-fractional Cattaneo-Maxwell heat equations, providing insights into wave propagation and dispersion characteristics in dissipative media, especially in fractional models.

Contribution

It offers a comprehensive analysis of dispersion relations and velocities for both classical and fractional Cattaneo-Maxwell heat equations, highlighting differences in wave behavior.

Findings

Dispersion relations are fully characterized for both models.

Group and phase velocities are explicitly derived.

Fractional models exhibit unique dispersion properties.

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.