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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 5123240, 8 pages
Research Article

Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function

1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2LaSIE, Pôle Sciences et Technologies, Université de La Rochelle, avenue M. Crépeau, 17042 La Rochelle Cedex, France

Correspondence should be addressed to Bessem Samet; as.ude.usk@temasb

Received 2 January 2017; Revised 19 January 2017; Accepted 22 January 2017; Published 12 February 2017

Academic Editor: Thabet Abdeljawad

Copyright © 2017 Mohamed Jleli et al. 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.


We consider a fractional boundary value problem involving a fractional derivative with respect to a certain function . A Hartman-Wintner-type inequality is obtained for such problem. Next, several Lyapunov-type inequalities are deduced for different choices of the function . Moreover, some applications to eigenvalue problems are presented.