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Zbl 1200.34004
Băleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.
An existence result for a superlinear fractional differential equation.
(English)
[J] Appl. Math. Lett. 23, No. 9, 1129-1132 (2010). ISSN 0893-9659

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 2000:
*34A08
34B15 Nonlinear boundary value problems of ODE

Keywords: sequential differential equation; Emden-Fowler equation; nonlinear oscillation

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