## Journal of Applied Mathematics

### The Existence of Solutions for a Fractional 2$m$-Point Boundary Value Problems

#### Abstract

By using the coincidence degree theory, we consider the following 2$m$-point boundary value problem for fractional differential equation ${D}_{0+}^{\alpha }u(t)=f(t,u(t),{D}_{0+}^{\alpha -1}u(t),{D}_{0+}^{\alpha -2}u(t))+e(t)$, $0, ${{I}_{0+}^{3-\alpha }u(t)|}_{t=0}=0,{D}_{0+}^{\alpha -2}u(1)={\sum }_{i=1}^{m-2}{a}_{i}{D}_{0+}^{\alpha -2}u({\xi }_{i}),u(1)={\sum }_{i=1}^{m-2}{b}_{i}u({\eta }_{i}),$ where $2<\alpha \le 3,$ ${D}_{0+}^{\alpha }$ and ${I}_{0+}^{\alpha }$ are the standard Riemann-Liouville fractional derivative and fractional integral, respectively. A new result on the existence of solutions for above fractional boundary value problem is obtained.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 841349, 18 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495023

Digital Object Identifier
doi:10.1155/2012/841349

Mathematical Reviews number (MathSciNet)
MR2872361

Zentralblatt MATH identifier
1241.34012

#### Citation

Wang, Gang; Liu, Wenbin; Yang, Jinyun; Zhu, Sinian; Zheng, Ting. The Existence of Solutions for a Fractional 2 $m$ -Point Boundary Value Problems. J. Appl. Math. 2012 (2012), Article ID 841349, 18 pages. doi:10.1155/2012/841349. https://projecteuclid.org/euclid.jam/1355495023