Microlocal analysis of fractional wave equations

TL;DR

This paper investigates the microlocal properties of solutions to specific fractional wave equations, revealing the behavior of singularities and propagation phenomena in space and time fractional contexts.

Contribution

It provides a detailed microlocal analysis of solutions to space and time fractional wave equations, highlighting differences in singularity propagation.

Findings

No spatial propagation of singularities in space fractional wave equation

Non-characteristic regularity in time fractional Zener wave equation

Distinct microlocal behaviors depending on fractional component

Abstract

We determine the wave front sets of solutions to two special cases of the Cauchy problem for the space-time fractional Zener wave equation, one being fractional in space, the other being fractional in time. For the case of the space fractional wave equation, we show that no spatial propagation of singularities occurs. For the time fractional Zener wave equation, we show an analogue of non-characteristic regularity.