Exploring Hermite–Hadamard-type Inequalities via ψ-conformable Fractional Integral Operators
DOI:
https://doi.org/10.63286/jima.2025.02Keywords:
Hermite-Hadamard type inequalities, ψ-conformable, convex functionAbstract
New Hermite-Hadamard inequalities for convex functions utilizing ψ-conformable fractional integral operators have been established. These represent extensions of many significant fractional operators, such as the Riemann-Liouville and Hadamard operators. Additionally, we establish generalized midpoint- and trapezoidal-type inequalities for these fractional integrals. These inequalities are expansions of other prior investigations.
References
[1] N. Azzouz, B. Benaissa, H. Budak, On generalized y-conformable calculus: properties and inequalities, Filomat, 38(25), 2024, 8755–8772.
DOI: 10.2298/FIL2425755A
[2] H. Budak, New Hermite–Hadamard-type inequalities for convex mappings utilizing generalized fractional integrals, Filomat, 33(8), 2019, 2329–2344.
DOI: 10.2298/FIL1908329B
[3] M. Jleli, B. Samet, On Hermite–Hadamard-type inequalities via fractional integrals of a function with respect to another function, Journal of Nonlinear Science and Applications, 9(3), 2016, 1252–1260.
[4] H. Kara, S. Erden, H. Budak, Hermite–Hadamard, trapezoid and midpoint type inequalities involving generalized fractional integrals for convex functions, Sahand Communications in Mathematical Analysis, 20(2), 2023, 85–107.
DOI: 10.22130/scma.2022.552775.1102
[5] U. N. Katugompola, New approach generalized fractional integral, Applied Mathematics and Computation, 218(3), 2011, 860–865.
DOI: 10.1016/j.amc.2011.03.062
[6] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 2014, 65–70.
DOI: 10.1016/j.cam.2014.01.002
[7] H. Li, B. Meftah, W. Saleh, H. Xu, A. Kiliçman, A. Lakhdari, Further Hermite–Hadamard-type inequalities for fractional integrals with exponential kernels, Fractal and Fractional, 8(6), 2024, 345.
DOI: 10.3390/fractalfract8060345
[8] M. Z. Sarikaya, H. Yildirim, On Hermite–Hadamard-type inequalities for Riemann-Liouville fractional integrals, Miskolc Mathematical Notes, 17(2), 2016, 1049–1059.
[9] E. Set, J. Choi, A. Gözpinar, Hermite–Hadamard-type inequalities involving nonlocal conformable fractional integrals, Malaysian Journal of Mathematical Sciences, 15(1), 2021, 33–43.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Noureddine Azzouz, Bouharket Benaissa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
