A study of nonlinear Langevin equation involving two fractional orders in different intervals

作者：Ahmad, Bashir^*; Nieto, Juan J.; Alsaedi, Ahmed; El-Shahed, Moustafa

来源：Nonlinear Analysis: Real World Applications , 2012, 13(2): 599-606.

DOI：10.1016/j.nonrwa.2011.07.052

• Langevin equation
• Fractional order
• Three-point boundary conditions
• Existence
• Fixed point

This paper studies a nonlinear Langevin equation involving two fractional orders alpha is an element of (0, 1] and beta is an element of (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.

• 出版日期2012-4