分数振荡器

从普通朗之万方程导出分数阶动力学

Fractional dynamics from the ordinary Langevin equation

我们考虑通常的朗之万方程依赖于一个内部时间。这个参数被一个自相似马尔可夫过程的第一次通过时间所取代。则高斯过程是父过程，命中时间过程是有向过程。在实时找到结果进程的概率由父进程和定向进程的概率密度之间的积分关系定义。相应的主方程变成分数福克-普朗克方程。我们证明了所得到的过程具有非马尔可夫性质，它的所有矩是有限的，波动耗散关系和H定理成立。

Subdiffusion equation with Caputo fractional derivative with respect to another function

We show an application of a subdiffusion equation with Caputo fractional time derivative with respect to another function $g$ to describe subdiffusion in a medium having a structure evolving over time. In this case a continuous transition from subdiffusion to other type of diffusion may occur. The process can be interpreted as "ordinary" subdiffusion with fixed subdiffusion parameter (subdiffusion exponent) $α$ in which time scale is changed by the function $g$. As example, we consider the transition from "ordinary" subdiffusion to ultraslow diffusion. The function $g$ generates the additional…

带关于另一函数的分数阶Caputo时间导数的次扩散方程在普通次扩散到超扩散转变建模中的应用

Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion

本研究提出带关于另一函数的分数阶Caputo时间导数的$g$-次扩散方程，通过构造合适的$g$函数和$g$-拉普拉斯变换求解，实现普通次扩散到超扩散的平滑转变，揭示其超扩散效应源于跳跃频率提升，且该方程具有普适性，可沿用普通次扩散的建模方法。

受保守噪声扰动的谐振子系统中能量的3/4分数超扩散

3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise

我们考虑一个谐波链的能量守恒噪声扰动，并表明，经过时空重新标度的能量-能量关联函数的指数为3/4的斜分数阶热方程的解决方案。

A comparative study of asymmetric dichotomous noise and symmetric trichotomous noise induced stochastic resonance in the globally coupled fractional oscillators

The collective behaviour, in respect of stochastic resonance, has been studied in globally coupled oscillators (with fractional-order intrinsic and external damping), driven by a sinusoidal force which is either noise-free or noise-modulated, and subjected to multiplicative quadratic asymmetric dichotomous or symmetric trichotomous noise perturbing the potential parameter, the coupling factor and the local drift force. The influence of coupling between the heat bath and the applied force has been included through a simple model. The effect of variation in mass, friction and potential parameter…

长程相互作用耦合振子的分数阶动力学

Fractional dynamics of coupled oscillators with long-range interaction

本文考虑一维耦合线性和非线性振子链的长程幂相互作用。动力学方程中的相应项与$1/|n-m|^{α+1}$成比例。证明了当$0<α<2$满足一定条件时，红外极限的运动方程可以转化为具有$α$阶Riesz分数阶导数的介质方程。我们考虑几个模型的耦合振荡器，并显示如何同步可以出现作为一个结果的分歧，以及如何相应的解决方案依赖于$α$。分数阶导数的存在也导致局域结构的出现。导出了分数阶含时复Ginzburg-Landau（或非线性Schrodinger）方程的特解。这些解决方案被解释为同步状态和局部结构的振荡介质。