Rad HAZU, Matematičke znanosti, Vol. 22 (2018), 77-91.

WEIGHTED HARDY-TYPE INEQUALITIES INVOLVING FRACTIONAL CALCULUS OPERATORS

Sajid Iqbal, Josip Pečarić, Muhammad Samraiz and Živorad Tomovski

Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia
e-mail: pecaric@element.hr

Department of Mathematics, University of Sargodha, Sargodha, Pakistan
e-mail: msamraiz@uos.edu.pk

Faculty of Mathematics and Natural Sciences, Gazi Baba bb, 1000 Skopje, Macedonia
e-mail: tomovski@pmf.ukim.mk

Abstract.   The aim of this paper is to give a new class of general weighted Hardy-type inequalities involving an arbitrary convex function with some applications of generalized fractional calculus convolutive operators which contain Gauss-hypergeometric function, generalized Mittag-Leffler function and Hilfer fractional derivative operator, in the kernel.

2010 Mathematics Subject Classification.   26D15, 26D10, 26A33, 34B27.

Key words and phrases.   Inequalities, convex function, fractional derivatives, generalized fractional integral operator.

DOI: https://doi.org/10.21857/ydkx2cr509

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