Existence of solutions to nonlinear Langevin equation involving two fractional orders with boundary value conditions.

*(English)*Zbl 1228.34016Authors’ abstract: We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnosel’skii’s fixed point theorem are applied to establish the existence results.

Reviewer: Li Changpin (Logan)

##### MSC:

34A08 | Fractional ordinary differential equations |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

47N20 | Applications of operator theory to differential and integral equations |

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\textit{A. Chen} and \textit{Y. Chen}, Bound. Value Probl. 2011, Article ID 516481, 17 p. (2011; Zbl 1228.34016)

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