Opuscula Math. 31, no. 3 (2011), 359-372
http://dx.doi.org/10.7494/OpMath.2011.31.3.359
Opuscula Mathematica
Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation
Xiaoyan Dou
Yongkun Li
Ping Liu
Abstract. In this paper, we discuss a four-point boundary value problem for a nonlinear differential equation of fractional order. The differential operator is the Riemann-Liouville derivative and the inhomogeneous term depends on the fractional derivative of lower order. We obtain the existence of at least one solution for the problem by using the Schauder fixed-point theorem. Our analysis relies on the reduction of the problem considered to the equivalent Fredholm integral equation.
Keywords: four-point boundary value problem, Riemann-Liouville fractional derivative, Green's function, Schauder fixed-point theorem.
Mathematics Subject Classification: 26A33, 34B10.
- Xiaoyan Dou
- Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. China
- Yongkun Li
- Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. China
- Ping Liu
- Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. China
- Received: 2010-06-14.
- Revised: 2010-07-21.
- Accepted: 2010-10-05.
