New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators
Abstract
:1. Introduction
2. Preliminaries
3. Main Results
4. Further Estimations via n-Polynomial Harmonically s-Type Convex Function
5. Conclusions and Future Scope
- (1)
- We presented and concentrated several fractional inequalities of the Caputo–Fabrizio operator for an n-polynomial s-type convex function and k-Riemann–Liouville fractional integral operator for an n-polynomial harmonically s-type convex function.
- (2)
- New version of Hermite–Hadamard inequality and Pachpatte-type inequality are obtained via Caputo–Fabrizio fractional integral operators.
- (3)
- Some special cases of the presented results have been in the form of corollaries and remarks.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Tariq, M.; Alsalami, O.M.; Shaikh, A.A.; Nonlaopon, K.; Ntouyas, S.K. New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators. Axioms 2022, 11, 618. https://doi.org/10.3390/axioms11110618
Tariq M, Alsalami OM, Shaikh AA, Nonlaopon K, Ntouyas SK. New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators. Axioms. 2022; 11(11):618. https://doi.org/10.3390/axioms11110618
Chicago/Turabian StyleTariq, Muhammad, Omar Mutab Alsalami, Asif Ali Shaikh, Kamsing Nonlaopon, and Sotiris K. Ntouyas. 2022. "New Fractional Integral Inequalities Pertaining to Caputo–Fabrizio and Generalized Riemann–Liouville Fractional Integral Operators" Axioms 11, no. 11: 618. https://doi.org/10.3390/axioms11110618