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International Journal of Mathematics and Mathematical Sciences
Volume 31, Issue 2, Pages 85-95

Opial type Lp-inequalities for fractional derivatives

1Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA
2Department of Mathematics and Statistics, University of Melbourne, Melbourne, VIC 3010, Australia
3Faculty of Textile Technology, University of Zagreb, Zagreb 10 000, Croatia

Received 7 May 2001; Revised 18 December 2001

Copyright © 2002 Hindawi Publishing Corporation. 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 presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives.