Authors: Atanacković, Teodor
Konjik, Sanja
Pilipović, Stevan
Zorica, Dušan 
Title: Complex order fractional derivatives in viscoelasticity
Journal: Mechanics of Time-Dependent Materials
Volume: 20
Issue: 2
First page: 175
Last page: 195
Issue Date: 1-Jun-2016
Rank: M21
ISSN: 1385-2000
DOI: 10.1007/s11043-016-9290-3
Abstract: 
We introduce complex order fractional derivatives in models that describe viscoelastic materials. This cannot be carried out unrestrictedly, and therefore we derive, for the first time, real valued compatibility constraints, as well as physical constraints that lead to acceptable models. As a result, we introduce a new form of complex order fractional derivative. Also, we consider a fractional differential equation with complex derivatives, and study its solvability. Results obtained for stress relaxation and creep are illustrated by several numerical examples.
Keywords: Constitutive equations | Real and complex order fractional derivatives | The Fourier transform | Thermodynamical restrictions | The Laplace transform
Publisher: Springer Link
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Provincial Secretariat for Science, Grant 114-451-1084

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