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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Series: | Advances in Difference Equations |
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Online Access: | https://doi.org/10.1186/s13662-020-03187-7 |
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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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