Existence and uniqueness of positive solution for a boundary value problem of fractional order.

*(English)*Zbl 1217.34009Summary: We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: \(D^{\alpha}_{0+}u(t) + f(t, u(t)) = 0, 0 \leq t \leq 1, 3 < \alpha \leq 4\), \(u(0) = u'(0) = u''(0) = u''(1) = 0\), where \(D^{\alpha}_{0+}\) denotes the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.

##### MSC:

34A08 | Fractional ordinary differential equations |

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\textit{J. Caballero} et al., Abstr. Appl. Anal. 2011, Article ID 165641, 12 p. (2011; Zbl 1217.34009)

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