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Some integral inequalities through tempered fractional integral operator

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

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
Year 2024, Volume: 73 Issue: 2, 399 - 409, 21.06.2024
https://doi.org/10.31801/cfsuasmas.1387622

Abstract

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
There are 24 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Research Articles
Authors

Erdal Gül 0000-0003-0626-0148

Abdüllatif Yalçın 0009-0003-1233-7540

Publication Date June 21, 2024
Submission Date November 8, 2023
Acceptance Date February 22, 2024
Published in Issue Year 2024 Volume: 73 Issue: 2

Cite

APA Gül, E., & Yalçın, A. (2024). Some integral inequalities through tempered fractional integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(2), 399-409. https://doi.org/10.31801/cfsuasmas.1387622
AMA Gül E, Yalçın A. Some integral inequalities through tempered fractional integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2024;73(2):399-409. doi:10.31801/cfsuasmas.1387622
Chicago Gül, Erdal, and Abdüllatif Yalçın. “Some Integral Inequalities through Tempered Fractional Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 2 (June 2024): 399-409. https://doi.org/10.31801/cfsuasmas.1387622.
EndNote Gül E, Yalçın A (June 1, 2024) Some integral inequalities through tempered fractional integral operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 2 399–409.
IEEE E. Gül and A. Yalçın, “Some integral inequalities through tempered fractional integral operator”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 2, pp. 399–409, 2024, doi: 10.31801/cfsuasmas.1387622.
ISNAD Gül, Erdal - Yalçın, Abdüllatif. “Some Integral Inequalities through Tempered Fractional Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/2 (June 2024), 399-409. https://doi.org/10.31801/cfsuasmas.1387622.
JAMA Gül E, Yalçın A. Some integral inequalities through tempered fractional integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73:399–409.
MLA Gül, Erdal and Abdüllatif Yalçın. “Some Integral Inequalities through Tempered Fractional Integral Operator”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 2, 2024, pp. 399-0, doi:10.31801/cfsuasmas.1387622.
Vancouver Gül E, Yalçın A. Some integral inequalities through tempered fractional integral operator. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2024;73(2):399-40.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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