Linear Viscoelastic Responses: The Prony Decomposition Naturally Leads Into the Caputo-Fabrizio Fractional Operator

Frontiers in Physics

Hristov, Jordan Yankov¹ 

[1] Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Bulgaria

关键词: linear viscoelasticity;    response functions;    interconversion;    power-law response;    non power-law responses;    Prony series;    Caputo-Fabrizio operator;    viscoelasticity;    response;    Prony series;    Caputo-Fabrizio;    interconversion;    Linear viscoelasticity;    Response function;    Prony series;    Caputo-Fabrizio operator;    Interconversion;   

DOI  :  10.3389/fphy.2018.00135

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

The study refers the physical background and modelling of linear viscoelastic response functions and their reasonable relationships to the Caputo-Fabrizio fractional operator via the Prony (Dirichlet series) series decomposition. The problem of interconversion with power-law and exponential (single and multi-term functions) has been discussed. Special attentions have been paid on the Prony series decomposition approach, the related interconversion problems and the expression of the viscoelastic constitutive equations in terms of Caputo-Fabrizio fractional operator.

【 授权许可】

CC BY