Authors: Hörmann, Günther
Oparnica, Ljubica
Zorica, Dušan 
Title: Solvability and microlocal analysis of the fractional Eringen wave equation
Journal: Mathematics and Mechanics of Solids
Volume: 23
Issue: 10
First page: 1420
Last page: 1430
Issue Date: 1-Oct-2018
Rank: M21a
ISSN: 10812865
DOI: 10.1177/1081286517726371
Abstract: 
© The Author(s) 2017. 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.
Keywords: Cauchy problem | distributional solutions | Eringen constitutive equation | fractional derivatives | Wavefront set
Publisher: SAGE Journals
Project: Austrian Science Fund, Grant P25326
Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Secretariat for Science Higher Education of Vojvodina, Grant 142-451-2489

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