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Zbl 1238.34008
Ahmad, Bashir; Nieto, Juan J.; Alsaedi, Ahmed; El-Shahed, Moustafa
A study of nonlinear Langevin equation involving two fractional orders in different intervals. (English)
[J] Nonlinear Anal., Real World Appl. 13, No. 2, 599-606 (2012). ISSN 1468-1218

Summary: We study a nonlinear Langevin equation involving two fractional orders $\alpha \in (0,1]$ and $\beta \in (1,2]$ with three-point boundary conditions. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions for the problem. The existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. Some illustrative examples are also discussed.

MSC 2000:: *34A08
34B10 Multipoint boundary value problems

Keywords: Langevin equation; fractional order; three-point boundary conditions; existence; fixed point

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