Vitali Vougalter, Vitaly Volpert
On the solvability of some systems of integro-differential equations with anomalous diffusion
(144K, pdf)

ABSTRACT.  The article deals with the existence of solutions of a system of integro-differential equations in the case of anomalous diffusion with the Laplacian in a fractional power. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for non Fredholm elliptic operators in unbounded domains are used.