Table of Contents
ISRN Mathematical Analysis
Volume 2011, Article ID 385459, 12 pages
http://dx.doi.org/10.5402/2011/385459
Research Article

Positive Solutions for Boundary Value Problem of Nonlinear Fractional π‘ž -Difference Equation

1Department of Mathematics, Faculty of Arts and Sciences, Qassim-Unizah 51911, P.O. Box 3771, Saudi Arabia
2Department of Mathematics, Majmaah University, Al-Majmaah 11952, P.O. Box 566, Saudi Arabia

Received 17 January 2011; Accepted 24 February 2011

Academic Editor: G. L. Karakostas

Copyright © 2011 Moustafa El-Shahed and Farah M. Al-Askar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the existence of multiple positive solutions to the nonlinear π‘ž -fractional boundary value problem 𝑐 𝐷 π‘Ž π‘ž 𝑒 ( 𝑑 ) + π‘Ž ( 𝑑 ) 𝑓 ( 𝑒 ( 𝑑 ) ) = 0 , 0 ≀ 𝑑 ≀ 1 , 2 < π‘Ž ≀ 3 , 𝑒 ( 0 ) = 𝐷 2 π‘ž 𝑒 ( 0 ) = 0 , 𝛾 𝐷 π‘ž 𝑒 ( 1 ) + 𝛽 𝐷 2 π‘ž 𝑒 ( 1 ) = 0 , by using a fixed point theorem in a cone.