Some new Grüss inequalities associated with generalized fractional derivative

Sajid Iqbal; Muhammad Samraiz; Gauhar Rahman; Kottakkaran Sooppy Nisar; Thabet Abdeljawad; Sajid Iqbal; Muhammad Samraiz; Gauhar Rahman; Kottakkaran Sooppy Nisar; Thabet Abdeljawad

doi:10.3934/math.2023010

AIMS Mathematics

2023, Volume 8, Issue 1: 213-227. doi: 10.3934/math.2023010

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Research article

Some new Grüss inequalities associated with generalized fractional derivative

1.
Department of Mathematics & Statistics, Institute of Southern Punjab, Bosan Road, Multan, Pakistan
2.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
3.
Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
4.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
5.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, KSA
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 01 August 2022 Revised: 02 September 2022 Accepted: 07 September 2022 Published: 28 September 2022
MSC : 26D15, 26D10, 26A33, 34B27

In this paper, we prove several new integral inequalities for the $ k $-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences.
- Grüss-type inequalities,
- kernel,
- fractional derivative,
- Young's inequality
Citation: Sajid Iqbal, Muhammad Samraiz, Gauhar Rahman, Kottakkaran Sooppy Nisar, Thabet Abdeljawad. Some new Grüss inequalities associated with generalized fractional derivative[J]. AIMS Mathematics, 2023, 8(1): 213-227. doi: 10.3934/math.2023010

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Abstract

In this paper, we prove several new integral inequalities for the $ k $-Hilfer fractional derivative operator, which is a fractional calculus operator. As a result, we have a whole new set of fractional integral inequalities. For the generalized fractional derivative, we also use Young's inequality to find new forms of inequalities. Such conclusions for this novel and generalized fractional derivative are extremely useful and valuable in the domains of differential equations and fractional differential calculus, both of which have a strong connections to real-world situations. These findings may stimulate additional research in a variety of fields of pure and applied sciences.

References

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