Vitali Vougalter, Vitaly Volpert
Solvability of some integro-differential equations with anomalous diffusion in two dimensions
(148K, pdf)

ABSTRACT.  The article is devoted to 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 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.