Weighted Hardy-type inequalities involving convex function for fractional calculus operators

Weighted Hardy-type inequalities involving convex function for fractional calculus operators

The aim of this paper is to establish some new weighted Hardy-type inequalities involving convex and monotone convex functions using Hilfer fractional derivative and fractional integral operator with generalized Mittag-Leffler function in its kernel. We also discuss one dimensional cases of our rela...

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Main Authors: Sajid Iqbal, Josip Pečarić, Lars-Erik Persson, Zivorad Tomovski
Format: Article
Language:English
Published: Elsevier 2018-08-01
Series:Transactions of A. Razmadze Mathematical Institute
Online Access:http://www.sciencedirect.com/science/article/pii/S234680921730106X
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spelling doaj-d79d81a7f42049ecb2edb56f831cd53d2020-11-25T01:10:08ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922018-08-011722205222Weighted Hardy-type inequalities involving convex function for fractional calculus operatorsSajid Iqbal0Josip Pečarić1Lars-Erik Persson2Zivorad Tomovski3Department of Mathematics, University of Sargodha (Sub-Campus Mianwali), Mianwali, Pakistan; Corresponding author.Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, CroatiaDepartment of Mathematics, Luleå University of Technology, SE-971 87, Luleå, Sweden; UIT The Artic University of Norway, P.O. Box 385, N-8505, Narvik, Norway,Faculty of Mathematics and Natural Sciences, Gazi Baba bb, 1000 Skopje, MacedoniaThe aim of this paper is to establish some new weighted Hardy-type inequalities involving convex and monotone convex functions using Hilfer fractional derivative and fractional integral operator with generalized Mittag-Leffler function in its kernel. We also discuss one dimensional cases of our related results. As a special case of our general results we obtain the results of Iqbal et al. (2017). Moreover, the refinement of Hardy-type inequalities for Hilfer fractional derivative is also included. Keywords: Convex function, Kernel, Hilfer fractional derivatives, Fractional integralhttp://www.sciencedirect.com/science/article/pii/S234680921730106X
collection DOAJ
language English
format Article
sources DOAJ
author Sajid Iqbal
Josip Pečarić
Lars-Erik Persson
Zivorad Tomovski
spellingShingle Sajid Iqbal
Josip Pečarić
Lars-Erik Persson
Zivorad Tomovski
Weighted Hardy-type inequalities involving convex function for fractional calculus operators
Transactions of A. Razmadze Mathematical Institute
author_facet Sajid Iqbal
Josip Pečarić
Lars-Erik Persson
Zivorad Tomovski
author_sort Sajid Iqbal
title Weighted Hardy-type inequalities involving convex function for fractional calculus operators
title_short Weighted Hardy-type inequalities involving convex function for fractional calculus operators
title_full Weighted Hardy-type inequalities involving convex function for fractional calculus operators
title_fullStr Weighted Hardy-type inequalities involving convex function for fractional calculus operators
title_full_unstemmed Weighted Hardy-type inequalities involving convex function for fractional calculus operators
title_sort weighted hardy-type inequalities involving convex function for fractional calculus operators
publisher Elsevier
series Transactions of A. Razmadze Mathematical Institute
issn 2346-8092
publishDate 2018-08-01
description The aim of this paper is to establish some new weighted Hardy-type inequalities involving convex and monotone convex functions using Hilfer fractional derivative and fractional integral operator with generalized Mittag-Leffler function in its kernel. We also discuss one dimensional cases of our related results. As a special case of our general results we obtain the results of Iqbal et al. (2017). Moreover, the refinement of Hardy-type inequalities for Hilfer fractional derivative is also included. Keywords: Convex function, Kernel, Hilfer fractional derivatives, Fractional integral
url http://www.sciencedirect.com/science/article/pii/S234680921730106X
work_keys_str_mv AT sajidiqbal weightedhardytypeinequalitiesinvolvingconvexfunctionforfractionalcalculusoperators
AT josippecaric weightedhardytypeinequalitiesinvolvingconvexfunctionforfractionalcalculusoperators
AT larserikpersson weightedhardytypeinequalitiesinvolvingconvexfunctionforfractionalcalculusoperators
AT zivoradtomovski weightedhardytypeinequalitiesinvolvingconvexfunctionforfractionalcalculusoperators
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