Vitali Vougalter, Vitaly Volpert
Solvability of some integro-differential equations with anomalous diffusion
(306K, pdf)

ABSTRACT.  The paper is devoted to the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the 
Laplace operator in a fractional power. The proof of existence of 
solutions relies on a fixed point technique. Solvability conditions 
for elliptic operators without Fredholm property in unbounded domains 
are used.