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.
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Acknowledgements
We would like to thank Marko Janev for several helpful discussions on the subject.
This work is supported by Projects 174005 and 174024 of the Serbian Ministry of Science, and 114-451-1084 of the Provincial Secretariat for Science.
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Atanacković, T.M., Konjik, S., Pilipović, S. et al. Complex order fractional derivatives in viscoelasticity. Mech Time-Depend Mater 20, 175–195 (2016). https://doi.org/10.1007/s11043-016-9290-3
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DOI: https://doi.org/10.1007/s11043-016-9290-3