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 as a function of the order of the space fractional derivative.