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.

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Cite this article as:
Xiaoyan Dou, Yongkun Li, Ping Liu, Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation, Opuscula Math. 31, no. 3 (2011), 359-372, http://dx.doi.org/10.7494/OpMath.2011.31.3.359

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