An existence result for a superlinear fractional differential equation

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