分数阶系统复杂性演化的随机性
The Stochastic Nature of Complexity Evolution in the Fractional Systems
摘要：
给出了复杂系统中松弛的随机情形。它是基于一般概率形式主义的极限定理。非指数松弛的结果从渐近自相似性质的时间行为，这样的系统。这个模型提供了一个严格的理由的能量标准介绍Jonscher。阐明了经验响应函数中参数的含义。这种处理揭示了一个新的光的性质，不仅介电弛豫，但也机械，发光和放射化学的。在科尔-科尔响应的情况下，分数阶导数的符号（经常出现在分数阶宏观方程中）和模型之间存在直接联系。但与Cole-Davidson和Havriliak-Negami弛豫有关的宏观响应方程，与普通的分数阶方程相比，具有更一般的积分-微分形式。
英文摘要：
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in the temporal behavior of such systems. This model provides a rigorous justification of the energy criterion introduced by Jonscher. The meaning of the parameters into the empirical response functions is clarified. This treatment sheds a fresh light on the nature of not only the dielectric relaxation but also mechanical, luminescent and radiochemical ones. In the case of the Cole-Cole response there exists a direct link between the notation of the fractional derivative (appearing in the fractional macroscopic equation often proposed) and the model. But the macroscopic response equations, relating to the Cole-Davidson and Havriliak-Negami relaxations, have a more general integro-differential form in comparison with the ordinary fractional one.
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