Solvability of some integro-differential equations with anomalous diffusion and transport

The article deals with the existence of solutions of an integro-differential equation in the case of anomalous diffusion with the negative Laplace operator in a fractional power in the presence of the transport term. The proof of existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used. We discuss how the introduction of the transport term impacts the regularity of solutions. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.