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Abstract and Applied Analysis
Volume 2012, Article ID 391062, 17 pages
Research Article

On a Differential Equation Involving Hilfer-Hadamard Fractional Derivative

Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 27 December 2011; Revised 10 April 2012; Accepted 14 April 2012

Academic Editor: Bashir Ahmad

Copyright © 2012 M. D. Qassim 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.


This paper studies a fractional differential inequality involving a new fractional derivative (Hilfer-Hadamard type) with a polynomial source term. We obtain an exponent for which there does not exist any global solution for the problem. We also provide an example to show the existence of solutions in a wider space for some exponents.