An existence result for a superlinear fractional differential equation

We establish the existence and uniqueness of solution for the boundary value problem 0Dtα(x′)+a(t)xλ=0, t>0t>0, x′(0)=0x′(0)=0, limt→+∞x(t)=1limt→+∞x(t)=1, where 0Dtα designates the Riemann–Liouville derivative of order α∈(0,1)α∈(0,1) and λ>1λ>1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden–Fowler equations.