## 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
$_0 D^{\alpha}_{t} (x^{\prime}) + a(t)x^{\lambda}, t>0, x^{\prime}(0) = 0, \lim_{t \rightarrow +\infty }x(t)=1,$
where $$_0 D^{\alpha}_t$$ designates the Riemann-Liouville derivative of order $$\alpha \in (0,1)$$ and $$\lambda >1$$. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equations.

### MSC:

 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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