论文标题
一类分数反应扩散方程的相似解决方案
Similarity solutions for a class of Fractional Reaction-Diffusion equation
论文作者
论文摘要
这项工作研究了一类分数反应扩散方程与Riemann-Liouville分数衍生物在半线上的相似性解决方案的确切可溶性。我们得出了公式具有比例对称性的条件，即使是分数衍生物。确定缩放指数之间的关系，并引入适当的相似性变量。随着相似性变量，我们将随机部分微分方程降低为分数的普通微分方程。然后，通过将所得的普通微分方程与已知的可溶解分数匹配来确定可溶解的系统。列出了涉及三参数Mittag-Leffler功能的几个示例（Kilbas-Saigo函数）。这里讨论的模型与超级延期系统相对应。
This work studies exact solvability of a class of fractional reaction-diffusion equation with the Riemann-Liouville fractional derivatives on the half-line in terms of the similarity solutions. We derived the conditions for the equation to possess scaling symmetry even with the fractional derivatives. Relations among the scaling exponents are determined, and the appropriate similarity variable introduced. With the similarity variable we reduced the stochastic partial differential equation to a fractional ordinary differential equation. Exactly solvable systems are then identified by matching the resulted ordinary differential equation with the known exactly solvable fractional ones. Several examples involving the three-parameter Mittag-Leffler function (Kilbas-Saigo function) are presented. The models discussed here turn out to correspond to superdiffusive systems.
