# Solvability and microlocal analysis of the fractional Eringen wave equation

## TL;DR

This paper investigates the existence, uniqueness, and microlocal regularity of solutions to the fractional Eringen wave equation, a non-local model involving space-fractional derivatives, supported by numerical illustrations.

## Contribution

It provides new results on the solvability and microlocal properties of the fractional Eringen wave equation, extending classical models with fractional derivatives.

## Key findings

- Existence and uniqueness of Sobolev space solutions
- Microlocal regularity properties established
- Numerical examples demonstrate solution behavior depending on fractional order

## 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.