Existence of solutions for a four-point boundary value problem of a nonlinear fractional differential equation

• Main Authors: Xiaoyan Dou, Yongkun Li, Ping Liu
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2011-01-01
• Series: Opuscula Mathematica
• Subjects: four-point boundary value problem; Riemann-Liouville fractional derivative; Green's function; Schauder fixed-point theorem
• Online Access: http://www.opuscula.agh.edu.pl/vol31/3/art/opuscula_math_3125.pdf
• ISSN: 1232-9274

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.