We use the continuous time random walk to analyze the asymptotic behavior of the Caputo–Fabrizio time-fractional diffusion equation (CF-tFDE). By evaluating the diffusion limit of the Laplace–Fourier transform of the solution to the CF-tFDE, we prove that the long-time limiting governing equation satisfies an integer-order Fickian diffusion equation. Numerical experiments are presented to verify the theoretical results.

中文翻译：

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Caputo-Fabrizio 时间分数扩散方程的渐近行为分析

我们使用连续时间随机游走来分析 Caputo-Fabrizio 时间分数扩散方程 (CF-tFDE) 的渐近行为。通过评估CF-tFDE解的拉普拉斯-傅里叶变换的扩散极限，我们证明了长时限控制方程满足整数阶Fickian扩散方程。给出了数值实验来验证理论结果。