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Abstract
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.
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Details
1 School of School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou Jiangsu, China.
2 School of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu, China.