New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions

Sinan Aslan

New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions

Abstract

In this paper, we establish several new fractional integral inequalities for arithmetic–geometrically convex (AG-convex) and geometrically–arithmetic convex (GA-convex) functions by means of the Caputo–Fabrizio fractional integral operator. By combining the structural properties of generalized convexity with the nonsingular exponential kernel of the Caputo–Fabrizio operator, we derive new Hermite–Hadamard-type estimates that extend a number of existing integral inequalities in the literature. Furthermore, Hölder's inequality and Young's inequality are employed to obtain refined upper bounds under suitable assumptions. The obtained results unify and generalize several previously known inequalities for generalized convex functions and demonstrate the effectiveness of the Caputo–Fabrizio fractional framework in the study of integral inequalities. The presented approach provides a useful analytical technique for future investigations involving generalized convexity and fractional integral operators with nonsingular kernels.

Keywords

References

ABDELJAWAD, THABET. On conformable fractional calculus. Journal of Computational and Applied Mathematics, 2015, 279: 57-66.
ABDELJAWAD, THABET; BALEANU, DUMITRU. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. arXiv preprint arXiv:1607.00262, 2016.
ABDELJAWAD, THABET; BALEANU, DUMITRU. On fractional derivatives with exponential kernel and their discrete versions. Reports on Mathematical Physics, 2017, 80.1: 11-27.
AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. EKİNCİ, A. Some New Results for Different Kinds of Convex Functions CaputoFabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (92) ICMRS 2021.
AKDEMİR, A. O.; ASLAN, S.; ÇAKALOĞLU, M.N. SET, E. New Hadamard Type Integral Inequalities via Caputo-Fabrizio Fractional Operators. 4th International Conference on Mathematical and Related Sciences. Page (91) ICMRS 2021.
AKDEMİR, A. O.; ASLAN, S.; EKİNCİ, A. Novel Approaches for s-Convex Functions via Caputo-Fabrizio Fractional Integrals. Proceedings of IAM, 2022, 11.1: 3-16.
AKDEMIR, AHMET OCAK, et al. New general variants of Chebyshev type inequalities via generalized fractional integral operators. Mathematics, 2021, 9.2: 122.
AKDEMIR, AHMET OCAK; EKINCI, ALPER; SET, ERHAN. Conformable fractional integrals and related new integral inequalities. 2017.

ANDERSON, G.D; VAMANAMURTHY, M.K; VUORINEN, M.Generalized convexity and inequalities, J. Math. Anal. Appl., 335 (2007), 1294-1308.
ATANGANA, ABDON; BALEANU, DUMITRU. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408, 2016.
BULLEN, P.S. Handbook of Means and Their Inequalities,Math. Appl., vol. 560, Kluwer Academic Publishers, Dordrecht, 2003.
BULLEN, P.S; MITRINOVIC D.S; VASIC P.M. Means and Their Inequalities, Reidel, Dordrecht; 1988.
BUTT, SAAD IHSAN, et al. New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals. Advances in Difference Equations, 2020, 2020: 1-24.
CAPUTO, MICHELE; FABRIZIO, MAURO. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation & Applications, 2015, 1.2: 73-85.
EKINCI, ALPER; OZDEMIR, MUHAMET. Some new integral inequalities via Riemann-Liouville integral operators. Applied and computational mathematics, 2019, 18.3.
GÜRBÜZ, MUSTAFA, et al. Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities. Journal of Inequalities and Applications, 2020, 2020: 1-10.
NICULESCU, C. P. Convexity according to the geometric mean. Math. Inequal. Appl, 2000, 3(2), 155-167.
NICULESCU, C. P. Convexity according to means. Mathematical Inequalities and Applications, 2003, 6, 571-580.
PEČARIĆ, JOSIP E. ; TONG, YUNG LIANG. Convex functions, partial orderings, and statistical applications. Academic Press, 1992.
RASHID, SAIMA, et al. New investigation on the generalized K-fractional integral operators. Frontiers in Physics, 2020, 8: 25.
RASHID, SAIMA, et al. New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating ℏ-convex functions in Hilbert space. Symmetry, 2020, 12.2: 222.
SAMKO, STEFAN G., et al. Fractional integrals and derivatives. Yverdon-les-Bains, Switzerland: Gordon and breach science publishers, Yverdon, 1993.
SET, ERHAN. New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals. Computers & Mathematics with Applications, 2012, 63.7: 1147-1154.
SET, ERHAN; AKDEMIR, AHMET OCAK; ÖZDEMIR, EMİN. M. Simpson type integral inequalities for convex functions via Riemann-Liouville integrals. Filomat, 2017, 31.14: 4415-4420.
TARIQ, MUHAMMAD, et al. New fractional integral inequalities for preinvex functions involving caputo fabrizio operator. 2022.
TOADER, G. Some generalizations of the convexity. In Proceedings of the Colloquium on Approximation and Optimization. Cluj-Napoca: University of Cluj-Napoca, 1985, (Vol. 329, p. 338).

Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis

Journal Section

Research Article

Authors

Sinan Aslan ^*
0000-0001-5970-1926
Türkiye

Publication Date

October 18, 2026

Submission Date

July 13, 2026

Acceptance Date

August 9, 2026

Published in Issue

Year 2026 Volume: 12 Number: 1

IZ

https://izlik.org/JA77NH87ZU

Cite

RIS / Bibtex

APA

Aslan, S. (2026). New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science, 12(1), 16-24. https://izlik.org/JA77NH87ZU

AMA

1.Aslan S. New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science. 2026;12(1):16-24. https://izlik.org/JA77NH87ZU

Chicago

Aslan, Sinan. 2026. “New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions”. Eastern Anatolian Journal of Science 12 (1): 16-24. https://izlik.org/JA77NH87ZU.

EndNote

Aslan S (October 1, 2026) New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science 12 1 16–24.

IEEE

[1]S. Aslan, “New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions”, Eastern Anatolian Journal of Science, vol. 12, no. 1, pp. 16–24, Oct. 2026, [Online]. Available: https://izlik.org/JA77NH87ZU

ISNAD

Aslan, Sinan. “New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions”. Eastern Anatolian Journal of Science 12/1 (October 1, 2026): 16-24. https://izlik.org/JA77NH87ZU.

JAMA

1.Aslan S. New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science. 2026;12:16–24.

MLA

Aslan, Sinan. “New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions”. Eastern Anatolian Journal of Science, vol. 12, no. 1, Oct. 2026, pp. 16-24, https://izlik.org/JA77NH87ZU.

Vancouver

1.Sinan Aslan. New Fractional Integral Inequalities for AG-Convex and GA-Convex Functions. Eastern Anatolian Journal of Science [Internet]. 2026 Oct. 1;12(1):16-24. Available from: https://izlik.org/JA77NH87ZU