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An existence result for a superlinear fractional differential equation. (English) Zbl 1200.34004

Summary: We establish the existence and uniqueness of solution for the boundary value problem

0 D t α (x ' )+a(t)x λ ,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.

MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
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