Vitali Vougalter
Solvability of some integro-differential equations with anomalous diffusion in higher dimensions
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ABSTRACT.  The article deals with the studies of 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 R^d, d=4,5. The proof of the existence of solutions relies on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used.