## Abstract

We discuss the existence of positive solutions to a class of fractional boundary value problem with changing sign nonlinearity and advanced arguments $$ $x(\mathrm{0})={\mathrm{x}}^{\mathrm{\prime}}(\mathrm{0})=\mathrm{0},$ $x(\mathrm{1})=\beta x(\eta )+\lambda [x],\mathrm{}\mathrm{}\mathrm{}\mathrm{}\beta >\mathrm{0},\; and\mathrm{}\mathrm{}\mathrm{}\mathrm{}\eta \in (\mathrm{0,1}),$ where ${D}^{\alpha}$ is the standard Riemann-Liouville derivative, $f:[\mathrm{0},\mathrm{\infty})\to [\mathrm{0},\mathrm{\infty})$ is continuous, $f(\mathrm{0})>\mathrm{0}$,$\mathrm{}\mathrm{}\mathrm{\hspace{0.17em}h\hspace{0.17em}}:[\mathrm{0,1}]\to (-\mathrm{\infty},+\mathrm{\infty})$, and $\mathrm{}\mathrm{}a(t)$ is the advanced argument. Our analysis relies on a nonlinear alternative of Leray-Schauder type. An example is given to illustrate our results.

## Citation

Zhaocai Hao. Yubo Huang. "Existence of Positive Solutions to Nonlinear Fractional Boundary Value Problem with Changing Sign Nonlinearity and Advanced Arguments." Abstr. Appl. Anal. 2014 (SI13) 1 - 7, 2014. https://doi.org/10.1155/2014/158436