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Discontinuity, Nonlinearity, and Complexity 5(3) (2016) 285--295 | DOI:10.5890/DNC.2016.09.007

Vitali Vougalter$^{1}$, Vitaly Volpert$^{2}$

$^{1}$ Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 2E4, Canada

$^{2}$ Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France

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Abstract

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.

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