Construction of new fractional inequalities via generalized $ n $-fractional polynomial $ s $-type convexity

Serap Özcan; Saad Ihsan Butt; Sanja Tipurić-Spužević; Bandar Bin Mohsin; Serap Özcan; Saad Ihsan Butt; Sanja Tipurić-Spužević; Bandar Bin Mohsin

doi:10.3934/math.20241163

AIMS Mathematics

2024, Volume 9, Issue 9: 23924-23944. doi: 10.3934/math.20241163

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Research article

Construction of new fractional inequalities via generalized $ n $-fractional polynomial $ s $-type convexity

1.
Department of Mathematics, Faculty of Sciences and Arts, Kırklareli University, Kırklareli, Turkey
2.
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
3.
Faculty of Chemistry and Technology, University of Split, Rudera Boškovića 35, Split 21000, Croatia
4.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 20 March 2024 Revised: 19 July 2024 Accepted: 25 July 2024 Published: 12 August 2024
MSC : 26D10, 26D15, 26E60, 90C23

This paper focuses on introducing and investigating the class of generalized $ n $-fractional polynomial $ s $-type convex functions within the framework of fractional calculus. Relationships between the novel class of functions and other kinds of convex functions are given. New integral inequalities of Hermite-Hadamard and Ostrowski-type are established for our novel generalized class of convex functions. Using some identities and fractional operators, new refinements of Ostrowski-type inequalities are presented for generalized $ n $-fractional polynomial $ s $-type convex functions. Some special cases of the newly obtained results are discussed. It has been presented that, under some certain conditions, the class of generalized $ n $-fractional polynomial $ s $-type convex functions reduces to a novel class of convex functions. It is interesting that, our results for particular cases recaptures the Riemann-Liouville fractional integral inequalities and quadrature rules. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes, and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.
- convex function,
- $ n $-fractional polynomial convex function,
- Hermite-Hadamard inequality,
- Ostrowski inequality,
- integral inequalities
Citation: Serap Özcan, Saad Ihsan Butt, Sanja Tipurić-Spužević, Bandar Bin Mohsin. Construction of new fractional inequalities via generalized $ n $-fractional polynomial $ s $-type convexity[J]. AIMS Mathematics, 2024, 9(9): 23924-23944. doi: 10.3934/math.20241163

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Abstract

This paper focuses on introducing and investigating the class of generalized $ n $-fractional polynomial $ s $-type convex functions within the framework of fractional calculus. Relationships between the novel class of functions and other kinds of convex functions are given. New integral inequalities of Hermite-Hadamard and Ostrowski-type are established for our novel generalized class of convex functions. Using some identities and fractional operators, new refinements of Ostrowski-type inequalities are presented for generalized $ n $-fractional polynomial $ s $-type convex functions. Some special cases of the newly obtained results are discussed. It has been presented that, under some certain conditions, the class of generalized $ n $-fractional polynomial $ s $-type convex functions reduces to a novel class of convex functions. It is interesting that, our results for particular cases recaptures the Riemann-Liouville fractional integral inequalities and quadrature rules. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes, and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields.

References

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