In this paper, we analyze the restrictions on the coefficients in the constitutive equations of linear Viscoelasticity that follow from the Second Law of Thermodynamics under isothermal conditions. Especially, we analyze the constitutive equations in which fractional derivatives of real and complex order appear. We present the conditions that follow after application of the Bochner–Schwartz theorem. Conditions derived here, representing in certain cases a weak form of the Second law of Thermodynamics, are more general (weaker) than the classical Bagley–Torvik conditions widely used in Viscoelasticity Theory. Several examples that illustrate the theory are presented.

中文翻译：

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分数阶的粘弹性：本构方程的新限制与应用

在本文中，我们分析了等温条件下热力学第二定律对线性粘弹性本构方程中系数的限制。特别是，我们分析了实数和复数阶分数导数出现的本构方程。我们提出了应用 Bochner-Schwartz 定理之后的条件。这里导出的条件，在某些情况下代表热力学第二定律的弱形式，比粘弹性理论中广泛使用的经典 Bagley-Torvik 条件更普遍（更弱）。举几个例子来说明这个理论。