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BibTex RIS Kaynak Göster

Yıl 2021, Cilt: 70 Sayı: 2, 900 - 909, 31.12.2021

Aysun Selçuk Kızılsu , Ayşe Feza Güvenilir

https://doi.org/10.31801/cfsuasmas.773392

Öz

Kaynakça

  • Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015), 57-66. https://doi:101016/j.cam.2014.10.016
  • Anderson, D. R., Ulness, D. J., Newly de…ned conformable derivatives, Advances in Dynamical Systems and Applications, 10(2) (2015), 109-137.
  • Beckenbach, E. F., Bellman, R., Inequalities, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.
  • Belarbi, S., Dahmani, Z., On some new fractional integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 10(3) (2009), Article 86, 5 pp.
  • Butt, S. I., Umar, M., Rashid, S., Akdemir, A. O., Chu, Y., New Hermite-Jensen-Mercer-type inequalities via k-fractional integrals, Advances in Difference Equations, (2020), Article 635, 24 pp. https://doi:10.1186/s13662-020-03093-y
  • Chebyshev, P. L., Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites, Proc. Math. Soc. Charkov, 2 (1882), 93-98.
  • Chen, S., Rashid, S., Hammouch, Z., Noor, M. A., Ashraf, R., Chu, Y., Integral inequalities via Raina's fractional integrals operator with respect to a monotone function, Advances in Difference Equations, Volume 2020 (2020), Article 647, 20 pp. https://doi:10.1186/s13662-020-03108-8
  • Diethelm, K., The Analysis of Fractional Di¤erential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer-Verlag, Berlin, 2010.
  • Fink, A. M., An essay on the history of inequalities, Journal of Mathematical Analysis and Applications, 249(1) (2000), 118-134. https://doi:10.1006/jmaa.2000.6934
  • Hardy G. H., Littlewood J. E., Polya, G., Inequalities, Cambridge University Press, Cambridge, 1952.
  • Katugampola, U. N., A new fractional derivative with classical properties, (2014), 8 pp. arXiv:1410.6535v2
  • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65-70. https://doi:10.1016/j.cam.2014.01.002
  • Khan, Z. A., Rashid, S., Ashraf, R., Baleanu, D., Chu, Y., Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property, Advances in Difference Equations, Volume 2020 (2020), Article 657, 24 pp. https://doi:10.1186/s13662-020-03121-x
  • Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  • Mitrinovic, D. S., Analytic Inequalities. Springer-Verlag, Berlin-Heidelberg-New York, 1970.
  • Musraini, M., Efendi, R., Lily, E., Hidayah, P., Classical properties on conformable fractional calculus, Pure and Applied Mathematics Journal, 8(5) (2019), 83-87. https://doi:10.11648/j.pamj.20190805.11
  • Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
  • Rashid, S., Jarad, F., Noor, M. A., Kalsoom, H., Chu, Y., Inequalities by means of generalized proportional fractional integral operators with respect to another function, Mathematics, 7(12) (2019), Article 1225, 18 pp. https://doi:10.3390/math7121225
  • Rashid, S., Ahmad, H., Khalid, A., Chu, Y., On discrete fractional integral inequalities for a class of functions, Hindawi, Volume 2020 (2020), Article ID 8845867, 13 pp. https://doi:10.1155/2020/8845867
  • Samko, S. G., Kilbas, A. A., Marichev, O. I., Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993.
  • Set E., Akdemir A. O., Mumcu I., Chebyshev type inequalities for conformable fractional integrals, Miskolc Mathematical Notes, 20(2) (2019), 1227-1236. https://doi:10.18514/MMN.2019.2766

Chebyshev inequality on conformable derivative

Yıl 2021, Cilt: 70 Sayı: 2, 900 - 909, 31.12.2021

Aysun Selçuk Kızılsu , Ayşe Feza Güvenilir

https://doi.org/10.31801/cfsuasmas.773392

Öz

Integral inequalities are very important in applied sciences. Chebyshev's integral inequality is widely used in applied mathematics. First of all, some necessary definitions and results regarding conformable derivative are given in this article. Then we give Chebyshev inequality for simultaneously positive (or negative) functions using the conformable fractional derivative. We used the Gronwall inequality to prove our results, unlike other studies in the literature.

Anahtar Kelimeler

Conformable Derivative conformable integral Chebyshev inequality

Kaynakça

  • Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015), 57-66. https://doi:101016/j.cam.2014.10.016
  • Anderson, D. R., Ulness, D. J., Newly de…ned conformable derivatives, Advances in Dynamical Systems and Applications, 10(2) (2015), 109-137.
  • Beckenbach, E. F., Bellman, R., Inequalities, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.
  • Belarbi, S., Dahmani, Z., On some new fractional integral inequalities, Journal of Inequalities in Pure and Applied Mathematics, 10(3) (2009), Article 86, 5 pp.
  • Butt, S. I., Umar, M., Rashid, S., Akdemir, A. O., Chu, Y., New Hermite-Jensen-Mercer-type inequalities via k-fractional integrals, Advances in Difference Equations, (2020), Article 635, 24 pp. https://doi:10.1186/s13662-020-03093-y
  • Chebyshev, P. L., Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites, Proc. Math. Soc. Charkov, 2 (1882), 93-98.
  • Chen, S., Rashid, S., Hammouch, Z., Noor, M. A., Ashraf, R., Chu, Y., Integral inequalities via Raina's fractional integrals operator with respect to a monotone function, Advances in Difference Equations, Volume 2020 (2020), Article 647, 20 pp. https://doi:10.1186/s13662-020-03108-8
  • Diethelm, K., The Analysis of Fractional Di¤erential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer-Verlag, Berlin, 2010.
  • Fink, A. M., An essay on the history of inequalities, Journal of Mathematical Analysis and Applications, 249(1) (2000), 118-134. https://doi:10.1006/jmaa.2000.6934
  • Hardy G. H., Littlewood J. E., Polya, G., Inequalities, Cambridge University Press, Cambridge, 1952.
  • Katugampola, U. N., A new fractional derivative with classical properties, (2014), 8 pp. arXiv:1410.6535v2
  • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264 (2014), 65-70. https://doi:10.1016/j.cam.2014.01.002
  • Khan, Z. A., Rashid, S., Ashraf, R., Baleanu, D., Chu, Y., Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property, Advances in Difference Equations, Volume 2020 (2020), Article 657, 24 pp. https://doi:10.1186/s13662-020-03121-x
  • Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  • Mitrinovic, D. S., Analytic Inequalities. Springer-Verlag, Berlin-Heidelberg-New York, 1970.
  • Musraini, M., Efendi, R., Lily, E., Hidayah, P., Classical properties on conformable fractional calculus, Pure and Applied Mathematics Journal, 8(5) (2019), 83-87. https://doi:10.11648/j.pamj.20190805.11
  • Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
  • Rashid, S., Jarad, F., Noor, M. A., Kalsoom, H., Chu, Y., Inequalities by means of generalized proportional fractional integral operators with respect to another function, Mathematics, 7(12) (2019), Article 1225, 18 pp. https://doi:10.3390/math7121225
  • Rashid, S., Ahmad, H., Khalid, A., Chu, Y., On discrete fractional integral inequalities for a class of functions, Hindawi, Volume 2020 (2020), Article ID 8845867, 13 pp. https://doi:10.1155/2020/8845867
  • Samko, S. G., Kilbas, A. A., Marichev, O. I., Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993.
  • Set E., Akdemir A. O., Mumcu I., Chebyshev type inequalities for conformable fractional integrals, Miskolc Mathematical Notes, 20(2) (2019), 1227-1236. https://doi:10.18514/MMN.2019.2766
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Aysun Selçuk Kızılsu 0000-0003-3022-0728

Ayşe Feza Güvenilir 0000-0003-2670-5570

Yayımlanma Tarihi 31 Aralık 2021
Gönderilme Tarihi 24 Temmuz 2020
Kabul Tarihi 12 Nisan 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 2

Kaynak Göster

APA Selçuk Kızılsu, A., & Güvenilir, A. F. (2021). Chebyshev inequality on conformable derivative. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 900-909. https://doi.org/10.31801/cfsuasmas.773392
AMA Selçuk Kızılsu A, Güvenilir AF. Chebyshev inequality on conformable derivative. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2021;70(2):900-909. doi:10.31801/cfsuasmas.773392
Chicago Selçuk Kızılsu, Aysun, ve Ayşe Feza Güvenilir. “Chebyshev Inequality on Conformable Derivative”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 2 (Aralık 2021): 900-909. https://doi.org/10.31801/cfsuasmas.773392.
EndNote Selçuk Kızılsu A, Güvenilir AF (01 Aralık 2021) Chebyshev inequality on conformable derivative. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 900–909.
IEEE A. Selçuk Kızılsu ve A. F. Güvenilir, “Chebyshev inequality on conformable derivative”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 2, ss. 900–909, 2021, doi: 10.31801/cfsuasmas.773392.
ISNAD Selçuk Kızılsu, Aysun - Güvenilir, Ayşe Feza. “Chebyshev Inequality on Conformable Derivative”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (Aralık 2021), 900-909. https://doi.org/10.31801/cfsuasmas.773392.
JAMA Selçuk Kızılsu A, Güvenilir AF. Chebyshev inequality on conformable derivative. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:900–909.
MLA Selçuk Kızılsu, Aysun ve Ayşe Feza Güvenilir. “Chebyshev Inequality on Conformable Derivative”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 2, 2021, ss. 900-9, doi:10.31801/cfsuasmas.773392.
Vancouver Selçuk Kızılsu A, Güvenilir AF. Chebyshev inequality on conformable derivative. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):900-9.

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

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