Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half-Line

Abstract EN

We are interested in the following fractional boundary value problem: Dαu(t)+atuσ=0, t∈(0,∞), limt→0t2-αu(t)=0, limt→∞t1-αu(t)=0, where 1<α<2, σ∈(-1,1), Dα is the standard Riemann-Liouville fractional derivative, and a is a nonnegative continuous function on (0,∞) satisfying some appropriate assumptions related to Karamata regular variation theory.

Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution.

We also give a global behavior of such solution.