(m + 1)维非线性时间分数阶偏微分方程的不变子空间方法
Invariant subspace method for (m + 1)-dimensional non-linear time-fractional partial differential equations
AI总结：
本文首次将不变子空间方法推广至(m + 1)维非线性时间分数阶偏微分方程，通过(3 + 1)维方程验证其有效性，并利用所得不变子空间推导出由指数、三角、多项式和Mittag-Leffler函数组合的精确解。
摘要：
本文首次将不变子空间方法的理论推广到(m + 1)维非线性时间分数阶偏微分方程。更具体地说，通过(3 + 1)维广义非线性时间分数阶扩散-对流-波方程及适当的初始条件，系统地研究了该方法的适用性和有效性。这一系统研究为寻找上述方程的一大类具有不同维数的各类不变子空间提供了重要技术。此外，我们证明了所得不变子空间有助于推导各种精确解，这些解可以表示为指数函数、三角函数、多项式和著名的Mittag-Leffler函数的组合。
英文摘要：
In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method have been systematically investigated through the (3 + 1)-dimensional generalized non-linear time-fractional diffusion-convection-wave equation along with appropriate initial conditions. This systematic investigation provides an important technique to find a large class of various types of the invariant subspaces with different dimensions for the above-mentioned equation. Additionally, we have shown that the obtained invariant subspaces help to derive a variety of exact solutions that can be expressed as the combinations of exponential, trigonometric, polynomial and well-known Mittag-Leffler functions.
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