Banach Journal of Mathematical Analysis

On some Hardy-type inequalities for fractional calculus operators

Sajid Iqbal, Josip Pečarić, Muhammad Samraiz, and Zivorad Tomovski

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In this article we present applications of Hardy-type and refined Hardy-type inequalities for a generalized fractional integral operator involving the Mittag-Leffler function in its kernel and for the Hilfer fractional derivative using convex and monotone convex functions.

Article information

Banach J. Math. Anal., Volume 11, Number 2 (2017), 438-457.

Received: 9 April 2016
Accepted: 16 July 2016
First available in Project Euclid: 18 March 2017

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Zentralblatt MATH identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 26D15: Inequalities for sums, series and integrals 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

inequalities Hardy-type inequalities Mittag-Leffler function fractional integral Hilfer fractional derivative


Iqbal, Sajid; Pečarić, Josip; Samraiz, Muhammad; Tomovski, Zivorad. On some Hardy-type inequalities for fractional calculus operators. Banach J. Math. Anal. 11 (2017), no. 2, 438--457. doi:10.1215/17358787-0000012X.

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