Solvability of Some Integro-Differential Equations with Anomalous Diffusion in Two Dimensions

We study the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the negative Laplace operator in a fractional power in two dimensions. The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.