On invariant solutions of linear time-fractional diffusion-wave equations with variable coefficients

TL;DR

This paper uses Lie symmetry analysis to find invariant solutions of variable-coefficient time-fractional diffusion-wave equations, revealing exact solutions involving special functions like Mittag-Leffler, Wright, and Fox H-functions.

Contribution

It introduces a method to derive invariant solutions for variable-coefficient fractional diffusion-wave equations using symmetry analysis.

Findings

Derived infinitesimal symmetries for the equations.

Obtained exact solutions in terms of special functions.

Enhanced understanding of transport and wave phenomena in fractional systems.

Abstract

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed by anomalous diffusion while the fractional wave equation describes oscillations and wave propagation in various physical systems. In order to obtain exact invariant solutions of these equations, we firstly determine infinitesimal symmetries with respect to the variable coefficients of the equations. With the help of these symmetries, we then find solutions in terms of Mittag-Leffler functions, generalized Wright functions and Fox H-functions.