一类分数阶反应扩散方程的相似解
Similarity solutions for a class of Fractional Reaction-Diffusion equation
AI总结：
本研究针对半直线上带Riemann-Liouville分数阶导数的分数阶反应扩散方程，通过推导标度对称条件、引入相似变量将方程约化为分数阶常微分方程，匹配已知可解模型确定精确可解系统，给出相关示例并验证其对应超扩散系统。
摘要：
本研究从相似解的角度，探讨了半直线上带Riemann-Liouville（黎曼-刘维尔）分数阶导数的一类分数阶反应扩散方程的精确可解性。我们推导了即使存在分数阶导数，该方程仍具备标度对称性的条件，确定了各标度指数之间的关系，并引入了合适的相似变量。借助该相似变量，我们将随机偏微分方程约化为一个分数阶常微分方程，随后通过将所得常微分方程与已知的精确可解分数阶常微分方程进行匹配，确定了精确可解的系统。文中给出了若干涉及三参数Mittag-Leffler函数（Kilbas-Saigo函数）的示例，且所讨论的模型对应超扩散系统。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
