Solvability and microlocal analysis of the fractional Eringen wave equation

Abstract

We discuss unique existence and microlocal regularity properties of Sobolev space solutions to the fractional Eringen wave equation, initially given in the form of a system of equations in which the classical non-local Eringen constitutive equation is generalized by employing space-fractional derivatives. Numerical examples illustrate the shape of solutions in dependence of the order of the space-fractional derivative.

References in corpus (4)

• $L^2$-Stability of Traveling Wave Solutions to Nonlocal Evolution Equations
• Monotone waves for non-monotone and non-local monostable reaction-diffusion equations
• Microlocal analysis of fractional wave equations
• Existence and Stability of Traveling Waves for a Class of Nonlocal Nonlinear Equations

Cited by in corpus (2)

• Energy dissipation for hereditary and energy conservation for non-local fractional wave equations
• Fractional Burgers wave equation