论文标题
在多维空间中解散方程溶液的明确公式
The explicit formula for solution of anomalous diffusion equation in the multi-dimensional space
论文作者
论文摘要
本文旨在在无限域中的无限初始条件和无穷大的无限初始条件和消失的无限域中获得$ n $维异常扩散方程的显式解决方案。结果表明，该方程可以从抛物线内部差异方程中得出，其中内核为$ t^{ - α} e_ {1-α，1-α，1-α，1-α}（ - t^{1-α}），α\ in（in（0，1），$ e_ phere $ e_ {$ e_ {ag ag ins $ e_ n is n is n is n s n s n s n s n s n s n s n s n s n is米the。基于拉普拉斯（Laplace）和傅立叶（Fourier）改变了FOX H功能和卷积定理的特性，可获得异常扩散方程的显式解决方案。
This paper intends on obtaining the explicit solution of $n$-dimensional anomalous diffusion equation in the infinite domain with non-zero initial condition and vanishing condition at infinity. It is shown that this equation can be derived from the parabolic integro-differential equation with memory in which the kernel is $t^{-α}E_{1-α, 1-α}(-t^{1-α}),α\in(0, 1),$ where $E_{α, β}$ is the Mittag-Liffler function. Based on Laplace and Fourier transforms the properties of the Fox H-function and convolution theorem, explicit solution for anomalous diffusion equation is obtained.
