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Ahmad, Bashir; Nieto, Juan J.; Alsaedi, Ahmed; El-Shahed, Moustafa

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

Nonlinear Anal., Real World Appl. 13, No. 2, 599-606 (2012).
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.

Cited in 167 Documents

MSC:

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

Keywords:

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

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