分式非线性、线性和次线性死亡过程
Fractional Non-Linear, Linear and Sublinear Death Processes
摘要：
本文研究了非线性$\mathpzc{M}^ν(t)$，$t>0$，线性$M^ν(t)$，$t>0$和次线性$\mathfrak{M}^ν(t)$，$t>0$死亡过程的分式形式.分数引入取代通常的整数阶导数的差分微分方程管理的状态概率，与分数导数的意义上理解的Dzhrbashyan-卡普托。我们明确地导出了三个死亡过程的状态概率，并研究了相关的概率母函数和平均值。一个有用的从属关系也被证明，使我们能够表达的死亡过程的经典对应物的随机时间过程$T_{2 ν} (t)$，$t>0$的组合物。这个随机时间具有一维分布，它是分数阶扩散方程柯西问题的折叠解。
英文摘要：
This paper is devoted to the study of a fractional version of non-linear $\mathpzc{M}^ν(t)$, $t>0$, linear $M^ν(t)$, $t>0$ and sublinear $\mathfrak{M}^ν(t)$, $t>0$ death processes. Fractionality is introduced by replacing the usual integer-order derivative in the difference-differential equations governing the state probabilities, with the fractional derivative understood in the sense of Dzhrbashyan--Caputo. We derive explicitly the state probabilities of the three death processes and examine the related probability generating functions and mean values. A useful subordination relation is also proved, allowing us to express the death processes as compositions of their classical counterparts with the random time process $T_{2 ν} (t)$, $t>0$. This random time has one-dimensional distribution which is the folded solution to a Cauchy problem of the fractional diffusion equation.
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