Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

Abstract In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some ne...

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Main Authors: Samaira Naz, Muhammad Nawaz Naeem, Yu-Ming Chu
Format: Article
Language:English
Published: SpringerOpen 2021-01-01
Series:Advances in Difference Equations
Subjects:
Grüss inequality
k-Riemann–Liouville fractional integral
Generalized k-fractional derivative
k-gamma function
Online Access:https://doi.org/10.1186/s13662-020-03187-7
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spelling doaj-5d9da09e40c64624a77d9fbc3baf758a2021-01-10T12:52:23ZengSpringerOpenAdvances in Difference Equations1687-18472021-01-012021111610.1186/s13662-020-03187-7Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivativeSamaira Naz0Muhammad Nawaz Naeem1Yu-Ming Chu2Department of Mathematics, Government College UniversityDepartment of Mathematics, Government College UniversityDepartment of Mathematics, Huzhou UniversityAbstract In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.https://doi.org/10.1186/s13662-020-03187-7Grüss inequalityk-Riemann–Liouville fractional integralGeneralized k-fractional derivativek-gamma function
collection DOAJ
language English
format Article
sources DOAJ
author Samaira Naz
Muhammad Nawaz Naeem
Yu-Ming Chu
spellingShingle Samaira Naz
Muhammad Nawaz Naeem
Yu-Ming Chu
Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
Advances in Difference Equations
Grüss inequality
k-Riemann–Liouville fractional integral
Generalized k-fractional derivative
k-gamma function
author_facet Samaira Naz
Muhammad Nawaz Naeem
Yu-Ming Chu
author_sort Samaira Naz
title Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
title_short Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
title_full Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
title_fullStr Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
title_full_unstemmed Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative
title_sort some k-fractional extension of grüss-type inequalities via generalized hilfer–katugampola derivative
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2021-01-01
description Abstract In this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.
topic Grüss inequality
k-Riemann–Liouville fractional integral
Generalized k-fractional derivative
k-gamma function
url https://doi.org/10.1186/s13662-020-03187-7
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AT yumingchu somekfractionalextensionofgrusstypeinequalitiesviageneralizedhilferkatugampoladerivative
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