@article{8cd28c0f995d47f38d620ad09fa798fa,
title = "A generalised distributed-order Maxwell model",
abstract = "In this work, we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accurate description of complex fluids when a proper weighting function of the order of the derivatives is chosen. We discuss the connection between classical, fractional and viscoelastic models of distributed order and highlight the fundamental concepts that support these constitutive equations. We also derive the relaxation modulus, the storage and loss modulus and the creep compliance for specific weighting functions.",
keywords = "distributed order fractional derivatives, fractional calculus, Laplace transform, Maxwell model, viscoelasticity",
author = "Ferr{\'a}s, {Lu{\'i}s L.} and Morgado, {M. Lu{\'i}sa} and Magda Rebelo",
note = "Funding Information: This work was funded by national funds through the FCT‐Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). L.L. Ferr{\'a}s would also like to thank FCT for financial support through CMAT (Centre of Mathematics of the University of Minho) projects UIDB/00013/2020 and UIDP/00013/2020. M.L. Morgado aknowledges funding by FCT through projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/ IST‐ID, Center for Computational and Stochastic Mathematics, Instituto Superior T{\'e}cnico, University of Lisbon. Funding Information: This work was funded by national funds through the FCT-Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). L.L. Ferr{\'a}s would also like to thank FCT for financial support through CMAT (Centre of Mathematics of the University of Minho) projects UIDB/00013/2020 and UIDP/00013/2020. M.L. Morgado aknowledges funding by FCT through projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT/ IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior T{\'e}cnico, University of Lisbon. Publisher Copyright: {\textcopyright} 2022 John Wiley & Sons, Ltd.",
year = "2023",
month = jan,
day = "15",
doi = "10.1002/mma.8516",
language = "English",
volume = "46",
pages = "368--387",
journal = "Mathematical Methods in the Applied Sciences",
issn = "0170-4214",
publisher = "Wiley",
number = "1",
}