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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 19, 2013

Vectorial fractional integral inequalities with convexity

  • George Anastassiou EMAIL logo
From the journal Open Physics

Abstract

Here we present vectorial general integral inequalities involving products of multivariate convex and increasing functions applied to vectors of functions. As specific applications we derive a wide range of vectorial fractional inequalities of Hardy type. These involve the left and right: Erdélyi-Kober fractional integrals, mixed Riemann-Liouville fractional multiple integrals. Next we produce multivariate Poincaré type vectorial fractional inequalities involving left fractional radial derivatives of Canavati type, Riemann-Liouville and Caputo types. The exposed inequalities are of L p type, p ≥ 1, and exponential type.

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Published Online: 2013-12-19
Published in Print: 2013-10-1

© 2013 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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