We prove stability estimates for the spatially discrete, Galerkin solution of a fractional Fokker–Planck equation, improving on previous results in several respects. Our main goal is to establish that the stability constants are bounded uniformly in the fractional diffusion exponent α ∈ (0,1). In addition, we account for the presence of an inhomogeneous term and show a stability estimate for the gradient of the Galerkin solution. As a by-product, the proofs of error bounds for a standard finite element approximation are simplified.

中文翻译：

---

空间离散、亚扩散 Fokker-Planck 方程的均匀稳定性

我们证明了分数阶 Fokker-Planck 方程的空间离散 Galerkin 解的稳定性估计，在几个方面改进了先前的结果。我们的主要目标是建立稳定常数在分数扩散指数α ∈ (0,1) 中均匀有界。此外，我们考虑了非齐次项的存在，并显示了伽辽金解梯度的稳定性估计。作为副产品，标准有限元近似的误差界限的证明得到了简化。