论文标题
随时间延迟
Exact solutions of generalized non-linear time-fractional reaction-diffusion equations with time delay
论文作者
论文摘要
在本文中，我们提出了不变的子空间方法，以通过时间延迟来找到精确的时间折段偏微分方程（PDE）的解决方案。提出了一种算法的方法，该方法是通过时间延迟来找到通用非线性时间裂缝反应方程的不变子空间。我们表明，随时间延迟的分数反应扩散方程允许几个不变子空间，这些子空间进一步产生了几种不同的分析溶液。我们还演示了如何通过多个时间延迟得出时间分数PDE的精确解决方案。最后，我们将不变的子空间方法扩展到具有涉及时间延迟的非线性术语的更广义的时间分数PDE。
In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized non-linear time-fractional reaction-diffusion equations with time delay is presented. We show that the fractional reaction-diffusion equations with time delay admit several invariant subspaces which further yields several distinct analytical solutions. We also demonstrate how to derive exact solutions for time-fractional PDEs with multiple time delays. Finally, we extend the invariant subspace method to more generalized time-fractional PDEs with non-linear terms involving time delay.
