We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation. Furthermore, we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s in [0.5,1). We also present an application of the advection-diffusion equation to anomalous transport of solutes.

翻译：我们分析的是非局部的厌食性非局部扩散方程式的准确性。在非本地矢量综合微积分的血管中,确定加权和非加权非本地的厌食性非局部扩散操作员之间的等同性,我们将我们的分析应用到一组分级操作员,并对相应的厌食性异常扩散方程式的解决方案提出严格的估计。此外,我们将我们的分析推广到厌食性扩散-偏执性方程式,并证明[0.5,1]中分数订单的精准性。我们还将吸食性扩散方程式应用到溶液的反常运输中。