论文标题
关于Poincarè半平面上的广义分数扩散方程的注释
A note on generalized fractional diffusion equations on Poincarè half plane
论文作者
论文摘要
在本文中，我们研究了Poincarè半平面上的广义时间折射方程$ \ Mathbb {H} _2^+$。这里考虑的时间分数运算符是相对于另一个函数的函数的分数衍生物，可以通过从经典的caputo衍生物开始，从本质上讲，这可以通过可变量的确定性变化来获得。我们获得了$ \ mathbb {h} _2^+$上广义扩散方程的基本解决方案的明确表示，并提供了与时间变化的双曲线布朗尼运动有关的概率解释。最终，我们为非线性案例提供了一个明确的结果，该案例承认分离变量解决方案。
In this paper we study generalized time-fractional diffusion equations on the Poincarè half plane $\mathbb{H}_2^+$. The time-fractional operators here considered are fractional derivatives of a function with respect to another function, that can be obtained by starting from the classical Caputo-derivatives essentially by means of a deterministic change of variable. We obtain an explicit representation of the fundamental solution of the generalized-diffusion equation on $\mathbb{H}_2^+$ and provide a probabilistic interpretation related to the time-changed hyperbolic Brownian motion. We finally include an explicit result regarding the non-linear case admitting a separating variable solution.
