The General Kelvin Model and Poynting Model Based on the General Fractional Calculus

2018 4th International Conference on Environmental Science and Material Application

生态环境科学;材料科学

Xu, Yingjun^1 ; Cheng, Menghong^2 ; Huang, Ruike^1 ; Yu, Jianqi^1

School of School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, China^1

School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu, China^2

关键词: Fractional calculus;    Fractional derivatives;    Fractional order derivatives;    General Kelvin model;    Kelvin-Voigt;    Laplace transform method;    Mittag-Leffler functions;    Thomson;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/252/2/022151/pdf
DOI  :  10.1088/1755-1315/252/2/022151

来源: IOP

【 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.