# American Institute of Mathematical Sciences

2015, 2015(special): 615-620. doi: 10.3934/proc.2015.0615

## Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition

 1 Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475, United States, United States

Received  September 2014 Revised  May 2015 Published  November 2015

In this paper, we apply Krasnosel'skii's cone expansion and compression fixed point theorem to show the existence of at least one positive solution to the nonlinear fractional boundary value problem $D^\alpha_{0^+} u + a(t)f(u)=0$, $0 < t < 1$, $1 < \alpha \le 2$, satisfying boundary conditions $u(0)=D^\beta_{0^+} u(1)=0$, $0\le\beta\le1$.
Citation: Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615
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