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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

${}_{0}{D}_{t}^{\alpha }\left({x}^{\text{'}}\right)+a\left(t\right){x}^{\lambda },t>0,{x}^{\text{'}}\left(0\right)=0,\underset{t\to +\infty }{lim}x\left(t\right)=1,$

where ${}_{0}{D}_{t}^{\alpha }$ designates the Riemann-Liouville derivative of order $\alpha \in \left(0,1\right)$ 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 differential equations 34B15 Nonlinear boundary value problems for ODE
##### References:
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