On the Steady Solutions of Fractional Reaction-Diffusion Equations

Hossein Fazli, Fariba Bahrami

In this paper, we study the existence of weak solutions for stationary fractional reaction-diffusion equations with Riemann--Liouville boundary conditions. An appropriate fractional Hilbert space is introduced and a compact embedding theorem demonstrated. Existence results are established using generalized Weierstrass theorem and relatively simple techniques from nonlinear functional analysis.