The article is devoted to the studies of the existence of solutions of an integro-differential equation in the case of the double scale anomalous diffusion with the sum of the two negative Laplacians raised to two distinct fractional powers in \({\mathbb R}^{d}, \ d=4, 5\). The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for the non-Fredholm elliptic operators in unbounded domains are used.

中文翻译：

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一些高维双尺度反常扩散积分微分方程的可解性

本文致力于研究双尺度反常扩散情况下积分微分方程解的存在性，其中两个负拉普拉斯算子之和提升为 \({\mathbb R}^ 中的两个不同分数次方) {d},\d=4, 5\)。解存在性的证明基于不动点技术。使用无界域中非 Fredholm 椭圆算子的可解性条件。