We report on recent progress in the study of nonlinear diffusion equations involving
nonlocal, long-range diffusion effects. Our main concern is the so-called fractional porous …

Designing an optimum receiver for diffusion-based molecular communication in nano-
networks needs a well justified channel model. In this paper, we present a linear and time …

We study a nonlinear elliptic problem defined in a bounded domain involving fractional
powers of the Laplacian operator together with a concave—convex term. We completely …

In this work we study the following fractional critical problem (P λ)={(− Δ) su= λ u q+ u 2 s⁎−
1, u> 0 in Ω, u= 0 in R n∖ Ω, where Ω⊂ R n is a regular bounded domain, λ> 0, 0< s< 1 and …

We describe the mathematical theory of diffusion and heat transport with a view to including
some of the main directions of recent research. The linear heat equation is the basic …

We develop a theory of existence, uniqueness and regularity for the following porous
medium equation with fractional diffusion, with m> m⁎=(N− 1)/N, N⩾ 1 and f∈ L1 (RN). An …

We describe two models of flow in porous media including nonlocal (long-range) diffusion
effects. The first model is based on Darcy's law and the pressure is related to the density by …

Introduction During the last years the modeling of dynamical phenomena has been
advanced by including concepts borrowed from fractional order differential equations. The …

In this paper we study the fractional Schrödinger type equations (− Δ) s u+ V (x) u= f (x, u),
x∈ R N. The nonlinearity f is assumed to be asymptotically linear or superquadratic growth …

Hippocampal activity patterns representing movement trajectories are reactivated in
immobility and sleep periods, a process associated with memory recall, consolidation, and …