Complex order fractional derivatives in viscoelasticity
Analysis of PDEs
2016-05-10 v3
Abstract
We introduce complex order fractional derivatives in models that describe viscoelastic materials. This can not 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.
Cite
@article{arxiv.1407.8294,
title = {Complex order fractional derivatives in viscoelasticity},
author = {Teodor M. Atanacković and Sanja Konjik and Stevan Pilipović and Dušan Zorica},
journal= {arXiv preprint arXiv:1407.8294},
year = {2016}
}