On the Steady Solutions of Fractional Reaction-Diffusion Equations

Abstract

‎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.