Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function
Abstract We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive...
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Online Access: | http://link.springer.com/article/10.1186/s13662-020-03108-8 |
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doaj-1d11f57918424a1dbafa3838ede311c32020-11-25T04:11:21ZengSpringerOpenAdvances in Difference Equations1687-18472020-11-012020112010.1186/s13662-020-03108-8Integral inequalities via Raina’s fractional integrals operator with respect to a monotone functionShu-Bo Chen0Saima Rashid1Zakia Hammouch2Muhammad Aslam Noor3Rehana Ashraf4Yu-Ming Chu5School of Science, Hunan City UniversityDepartment of Mathematics, Government College UniversityDivision of Applied Mathematics, Thu Dau Mot UniversityDepartment of Mathematics, COMSATS University IslamabadDepartment of Mathematics, Lahore College Women University, Jhangh CampusDepartment of Mathematics, Huzhou UniversityAbstract We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive the Grüss and certain other associated variants by using well-known integral inequalities such as Young, Lah–Ribarič, and Jensen integral inequalities. In the concluding section, we present several special cases of fractional integral inequalities involving generalized Riemann–Liouville, k-fractional, Hadamard fractional, Katugampola fractional, ( k , s ) $(k,s)$ -fractional, and Riemann–Liouville-type fractional integral operators. Moreover, we also propose their pertinence with other related known outcomes.http://link.springer.com/article/10.1186/s13662-020-03108-8Grüss inequalityYoung inequalityGeneralized fractional integral operatorRaina function |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shu-Bo Chen Saima Rashid Zakia Hammouch Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu |
spellingShingle |
Shu-Bo Chen Saima Rashid Zakia Hammouch Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function Advances in Difference Equations Grüss inequality Young inequality Generalized fractional integral operator Raina function |
author_facet |
Shu-Bo Chen Saima Rashid Zakia Hammouch Muhammad Aslam Noor Rehana Ashraf Yu-Ming Chu |
author_sort |
Shu-Bo Chen |
title |
Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function |
title_short |
Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function |
title_full |
Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function |
title_fullStr |
Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function |
title_full_unstemmed |
Integral inequalities via Raina’s fractional integrals operator with respect to a monotone function |
title_sort |
integral inequalities via raina’s fractional integrals operator with respect to a monotone function |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2020-11-01 |
description |
Abstract We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration the generalized fractional integral with respect to a monotone function, we derive the Grüss and certain other associated variants by using well-known integral inequalities such as Young, Lah–Ribarič, and Jensen integral inequalities. In the concluding section, we present several special cases of fractional integral inequalities involving generalized Riemann–Liouville, k-fractional, Hadamard fractional, Katugampola fractional, ( k , s ) $(k,s)$ -fractional, and Riemann–Liouville-type fractional integral operators. Moreover, we also propose their pertinence with other related known outcomes. |
topic |
Grüss inequality Young inequality Generalized fractional integral operator Raina function |
url |
http://link.springer.com/article/10.1186/s13662-020-03108-8 |
work_keys_str_mv |
AT shubochen integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction AT saimarashid integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction AT zakiahammouch integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction AT muhammadaslamnoor integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction AT rehanaashraf integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction AT yumingchu integralinequalitiesviarainasfractionalintegralsoperatorwithrespecttoamonotonefunction |
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1724418021185814528 |