International Journal of Mathematics and Mathematical Sciences (Jan 2002)

Opial type Lp-inequalities for fractional derivatives

  • G. A. Anastassiou,
  • J. J. Koliha,
  • J. Pecaric

DOI
https://doi.org/10.1155/S016117120201311X
Journal volume & issue
Vol. 31, no. 2
pp. 85 – 95

Abstract

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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.