Generalized viscoelastic models: Their fractional equations with solutions
Generalized viscoelastic models: Their fractional equations with solutions
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DOI：
10.1088/0305-4470/28/23/012
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发表时间：
1995-12-07
期刊：
影响因子：
--
通讯作者：
Nonnenmacher, TF
中科院分区：
文献类型：
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作者：
Schiessel, H;Metzler, R;Nonnenmacher, TF
近年来分数阶微积分（FC）在复杂动力学的描述中取得了很大的成功。特别是铁已被证明是一个有价值的工具来处理粘弹性方面。本文在经典力学模型的基础上，特别是在麦克斯韦、Kelvin-Voigt、Zener和Poynting-Thomson模型的基础上，构造了分数阶流变本构方程。为此，我们引入一个分数元素，除了标准的纯弹性和纯粘性元素。正如我们继续表明，许多分数阶微分方程，我们得到了这种建设方法承认封闭形式，解析解的福克斯X-函数的米塔格-莱弗勒型。
Recently fractional calculus (FC) has encountered much success in the description of complex dynamics. In particular Fe has proved to be a valuable tool to handle viscoelastic aspects. In this paper we construct fractional theological constitutive equations on the basis of well known mechanical models, especially the Maxwell, the Kelvin-Voigt, the Zener and the Poynting-Thomson model. To this end we introduce a fractional element, in addition to the standard purely elastic and purely viscous elements. As we proceed to show, many of the fractional differential equations which we obtain by this construction method admit closed form, analytical solutions in terms of Fox X-functions of the Mittag-Leffler type.