文章基本信息

标题：The General Kelvin Model and Poynting Model Based on the General Fractional Calculus
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作者：Yingjun Xu ; Menghong Cheng ; Ruike Huang 等
期刊名称：IOP Conference Series: Earth and Environmental Science
印刷版ISSN：1755-1307
电子版ISSN：1755-1315
出版年度：2019
卷号：252
期号：2
页码：1-9
DOI：10.1088/1755-1315/252/2/022151
出版社：IOP Publishing
摘要：In this paper, the Riemann-Liouville fractional-order derivative definition without nonsingular power-law kernel is used as mathematical tool to describe the rheology models. Two fractional order coupling models which are the general Kelvin-Voigt and Poynting-Thomson are gradually discussed through Laplace transform method and Mittag-Leffler function. Meanwhile, the creep compliances and relaxation modulus via the Riemann-Liouville general fractional order derivative are also given. The models via the classical calculus could be regarded as a special situation compared with the two improved models proposed in this paper.