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Grüss-type inequalities involving functional bounds via analytic kernel fractional integral
Majid K Neamah1,2, Alawiah Ibrahim2, Tariq A Aljaaidi3
1Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq.
Methodsx
|September 24, 2025
Summary
This study generalizes Grüss-type inequalities using a novel fractional integral operator with analytic kernels. These advancements offer more effective mathematical tools for fractional calculus and its applications.
Area of Science:
- Fractional Calculus
- Mathematical Analysis
- Inequalities
Background:
- Grüss-type inequalities are fundamental in mathematical analysis.
- Existing inequalities often have limitations in functional bounds.
- Fractional calculus offers advanced tools for integral inequalities.
Purpose of the Study:
- To generalize Grüss-type inequalities for functional bounds.
- To introduce a generalized fractional integral with analytic kernels.
- To extend existing inequality research.
Main Methods:
- Utilized a generalized analytic kernel Riemann-Liouville fractional integral.
- Applied Young's Inequality and Cauchy-Schwarz Inequality.
- Investigated inequalities for single and distinct orders.
Main Results:
- Presented a generalized Grüss-type inequality using the novel fractional integral.
- Established rigorous bounds for functional inequalities.
- Discussed exceptional cases and derived corresponding results.
Conclusions:
- The generalized Grüss-type inequality enhances mathematical tools.
- The work facilitates broader applications in fractional calculus.
- Opens new research directions in complex fractional calculus.
Keywords:
Analytic kernel fractional integralFractional integralFunctional boundsGrüss type inequalitiesRiemann-Liouville fractional integralMore Related Videos
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