Some integral inequalities through tempered fractional integral operator

Year 2024, Volume: 73 Issue: 2, 399 - 409, 21.06.2024

Erdal Gül Abdüllatif Yalçın

https://doi.org/10.31801/cfsuasmas.1387622

Abstract

In this article, we adopt the tempered fractional integral operators to develop some novel Minkowski and Hermite-Hadamard type integral inequalities. Thus, we give several special cases of the integral inequalities for tempered fractional integrals obtained in the earlier works.

Keywords

Hermite-Hadamard type inequalities, Minkowski inequality, convex and concave functions, Riemann-Liouville integrals, tempered fractional integral

References

• Abramovich, S., Farid, G., Pecaric, J., More about Hermite-Hadamard inequalities, Cauchy’s means, and superquadracity, Journal of Inequalities and Applications, (2010), 102467. https://doi.org/10.1155/2010/102467
• Akdemir, A. O., Özdemir, M. E., Avcı Ardıç, M., Yalçın, A., Some new generalizations for GA-convex functions, Filomat, 31 (4) (2017), 1009-1016. https://doi.org/10.2298/fil1704009a
• Sarıkaya, M. Z., Set, E., Yaldız, H., Başak, N, Hermite-Hadamard inequalities for fractional integrals and related fractional inequalities, Mathematical and Computational Modelling, 57 (9-10), (2013), 2403-2407. https://doi.org/10.1016/j.mcm.2011.12.048
• Azpeitia, A. G., Convex functions and Hadamard inequality, Revista Colombiana de Matematicas, 28 (1), (1994), 7-12. https://doi.org/10.15446/recolma
• Akdemir, A. O., Set, E., Özdemir, M. E., Yalçın, A., New generalizations for functions with second GG-convex derivatives, Uzbek Mathematical Journal, 4 (2018). https://doi.org/10.29229/uzmj.2018-4-3
• Nonnenmacher, Theo F., Metzler., R., On the Riemann-Liouville fractional calculus and some recent applications, Fractals, 3 (03) (1995), 557-566. https://doi.org/10.1142/s0218348x95000497
• Buschman, R. G., A factorization of an integral operator using Mikusinski calculus, SIAM Journal on Mathematical Analysis, 3 (1), (1972), 83-85. https://doi.org/10.1137/0503010
• Liu, R., Wu, Z., Well-posedness of a class of two-point boundary value problems associated with ordinary differential equations, Adv. Differ. Equ. 2018, 54 (2018). https://doi.org/10.1186/s13662-018-1510-5
• Meerschaert, M. M., Sabzikar, F., Chen, J., Tempered fractional calculus, Journal of Computational Physics, 293 (2015), 14. https://doi.org/10.1016/j.jcp.2014.04.024
• Mohammed, P. O., Sarikaya, M. Z., Baleanu, D., On generalized Hermite-Hadamard inequalities via fractional integrals, Symmetry, 12 (4), (2020), 595. https://doi.org/10.3390/sym12040595
• Fernandez, A., Ustaoğlu, C., On some analytic properties of Hardened fractional calculus, Journal of Computational and Applied Mathematics, 366 (2020), 112400. https://doi.org/10.1016/j.cam.2019.112400
• Nisar, K.S., Tassaddiq, A., Rahman, G. et al., Some inequalities via fractional conformable integral operators, J Inequal Appl., 2019, 217 (2019). https://doi.org/10.1186/s13660-019-2170-z
• Gül, E., Akdemir, A., Yalçın, A., On Minkowski inequalities involving fractional analysis with general analytic kernels, arXiv preprint arXiv:2310.11221, 2023.
• Gül, E., Yalçın, A., Some new estimates for Hadamard-type inequalities for different types of convex functions using tempered fractional integral operators, Filomat, 38 (10), in press, (2024).
• İkinci, A., Eroğlu, N., New generalizations for convex functions via conformable fractional integrals, Filomat, 33 (14), (2019), 4525-4534. https://doi.org/10.2298/fil1914525e
• Gorenflo, R., Mainardi, F., Fractional Calculus: Integral and Differential Equations of Fractional Degree, In Fractals and Fractional Calculus in Continuum Mechanics (Udine, 1996), pp. 223–276. CISM Courses and Lectures, vol. 378, Springer, (1997).
• Oldham, K. B., Spanier, J., Fractional Calculus, Academic Press, (1974).
• Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Annals of Functional Analysis, 1(1), (2010), 51-58. https://doi.org/10.15352/afa/1399900993
• Bougoffa, L., On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 7(2), (2006), 60.
• Set, E., Özdemir, M. E., Dragomir, S. S., On Hermite-Hadamard inequality and other integral inequalities involving two functions, Journal of Inequalities and Applications, (2010), 1-9. https://doi.org/10.1155/2010/148102
• Set, E., Özdemir, M. E., Dragomir, S. S., On Hermite-Hadamard inequality and other integral inequalities involving two functions, Journal of Inequalities and Applications, (2010), 1-9. https://doi.org/10.1155/2010/148102
• Akdemir A.O., Aslan S., Dokuyucu, M. A., Celik E., Exponentially convex functions on the coordinates and novel estimations via Riemann-Liouville fractional operator, Journal of Function Spaces, vol.2023, art.n.4310880, (2023). 0, 9 pages, https://doi.org/10.1155/2023/4310880
• Akdemir A.O., Karaoglan A., Ragusa M.A., E. Set, Fractional integral inequalities via Atangana-Baleanu operators for convex and concave functions, Journal of Function Spaces, 2021, art. ID 1055434, (2021). https://doi.org/10.1155/2021/1055434
• Set E., Akdemir A.O., Ozdemir M.E., Karaoglan A., Dokuyucu M.A., New integral inequalities for Atangana-Baleanu fractional integral operators and various comparisons via simulations, Filomat, 37 (7), 2251-2267, (2023). https://doi.org/10.2298/FIL2307251S