## A study of nonlinear Langevin equation involving two fractional orders in different intervals.(English)Zbl 1238.34008

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:

 34A08 Fractional ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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### References:

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