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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
\[ _0 D^{\alpha}_{t} (x^{\prime}) + a(t)x^{\lambda}, t>0, x^{\prime}(0) = 0, \lim_{t \rightarrow +\infty }x(t)=1, \]
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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