On the Existence of Stationary Solutions for Some Systems of Integro-Differential Equations with Anomalous Diffusion - Vougalter, Vitali; Volpert, Vitaly (Discontinuity, Nonlinearity, and Complexity, 2026)
The article is devoted to the proof of the existence of solutions of a system of integro-differential equations appearing in the case of anomalous diffusion when the negative Laplacian is raised to some fractional power. The argument relies on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbounded domains along with the Sobolev inequality for a fractional Laplace operator are being used.