The Minkowski inequalities via generalized proportional fractional integral operators

Gauhar Rahman; Aftab Khan; Thabet Abdeljawad; Kottakkaran Sooppy Nisar

doi:10.1186/s13662-019-2229-7

The Minkowski inequalities via generalized proportional fractional integral operators

Gauhar Rahman
, Aftab Khan
, Thabet Abdeljawad
, Kottakkaran Sooppy Nisar

Mathematics

Research output: Contribution to journal › Article › peer-review

74 Scopus citations

Abstract

Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional integrals and derivatives lately introduced by Jarad et al. (Eur. Phys. J. Special Topics 226:3457–3471, 2017) comprising the exponential functions in the kernels. The principal aim of this paper is to establish reverse Minkowski inequalities and some other fractional integral inequalities by utilizing generalized proportional fractional integrals. Also, two new theorems connected with this inequality as well as other inequalities associated with the generalized proportional fractional integrals are established.

Original language	English
Article number	287
Journal	Advances in Difference Equations
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2229-7
State	Published - 1 Dec 2019

Keywords

Generalized proportional fractional integral operator
Inequality
Minkowski inequalities

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keywords = "Generalized proportional fractional integral operator, Inequality, Minkowski inequalities",

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AU - Khan, Aftab

AU - Abdeljawad, Thabet

AU - Nisar, Kottakkaran Sooppy

PY - 2019/12/1

Y1 - 2019/12/1

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AB - Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional integrals and derivatives lately introduced by Jarad et al. (Eur. Phys. J. Special Topics 226:3457–3471, 2017) comprising the exponential functions in the kernels. The principal aim of this paper is to establish reverse Minkowski inequalities and some other fractional integral inequalities by utilizing generalized proportional fractional integrals. Also, two new theorems connected with this inequality as well as other inequalities associated with the generalized proportional fractional integrals are established.

KW - Generalized proportional fractional integral operator

KW - Inequality

KW - Minkowski inequalities

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JO - Advances in Difference Equations

JF - Advances in Difference Equations

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ER -

The Minkowski inequalities via generalized proportional fractional integral operators

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