Microlocal analysis of fractional wave equations

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.

Cited by in corpus (5)

• Distributed order fractional constitutive stress-strain relation in wave propagation modeling
• Energy dissipation for hereditary and energy conservation for non-local fractional wave equations
• Micro-local and qualitative analysis of the fractional Zener wave equation
• Fractional Burgers wave equation
• Solvability and microlocal analysis of the fractional Eringen wave equation