Research Article

On new integral inequalities using mixed conformable fractional integrals

Volume: 69 Number: 2 December 31, 2020
EN

On new integral inequalities using mixed conformable fractional integrals

Abstract

During the past two decades or so, fractional integral operators have been one of the most important tools in the development of inequalities theory. By this means, a lot generalized intergral inequalities involving various the fractional integral operators have been presented in the literature. Very recently, mixed conformable fractional integral operators has been introduced by T. Abdeljawad and with the help of these operators some new integral inequalities are obtained. The main aim of the paper is to establish some new Chebyshev type fractional integral inequalities by using mixed conformable fractional integral operators.

Keywords

References

  1. Abdeljawad, T., Fractional operators with boundary points dependent kernels and integration by parts, Discrete and Continuous Dynamical Systems Series S, 13(3) (2020), 351-375.
  2. Baleanu, D., Purohit, S.D., Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators, Abstract and Applied Analysis, 2014 (2014), Article ID 609160, 1--10.
  3. Baleanu, D., Purohit, S.D., Prajapati, J.C., Integral inequalities involving generalized Erdélyi-Kober fractional integral operators, Open Mathematics, 14 (2016), 89--99.
  4. 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.
  5. Curiel, L., Galué, L., A generalization of the integral operators involving the Gauss hypergeometric function, Revista Técnica de la Facultad de Ingeniería Universidad del Zulia, 19(1) (1996), 17--22.
  6. Çelik, B., Set, E., Akdemir, A.O., Mixed Conformable Fractional Grüss-Type Inequalities, 2nd International Conference on Life and Engineering Sciences (ICOLES 2019), Book of Abstracts, Istanbul, Turkey, 2019.
  7. Dahmani, Z., Mechouar, O. and Brahami, S., Certain inequalities related to the Chebyshev's functional involving a Riemann-Liouville operator, Bull. Math. Anal. Appl., 3(4) (2011), 38--44.
  8. Ekinci, A., Özdemir, M.E., Some new integral Inequalities via Riemann Liouville integral operators, Applied and Computational Mathematics, 18(3) (2019), 288--295.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

December 31, 2020

Submission Date

March 5, 2020

Acceptance Date

May 30, 2020

Published in Issue

Year 2020 Volume: 69 Number: 2

APA
Çelik, B., & Set, E. (2020). On new integral inequalities using mixed conformable fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1057-1069. https://doi.org/10.31801/cfsuasmas.698841
AMA
1.Çelik B, Set E. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1057-1069. doi:10.31801/cfsuasmas.698841
Chicago
Çelik, Barış, and Erhan Set. 2020. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2): 1057-69. https://doi.org/10.31801/cfsuasmas.698841.
EndNote
Çelik B, Set E (December 1, 2020) On new integral inequalities using mixed conformable fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1057–1069.
IEEE
[1]B. Çelik and E. Set, “On new integral inequalities using mixed conformable fractional integrals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1057–1069, Dec. 2020, doi: 10.31801/cfsuasmas.698841.
ISNAD
Çelik, Barış - Set, Erhan. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 1, 2020): 1057-1069. https://doi.org/10.31801/cfsuasmas.698841.
JAMA
1.Çelik B, Set E. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1057–1069.
MLA
Çelik, Barış, and Erhan Set. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, Dec. 2020, pp. 1057-69, doi:10.31801/cfsuasmas.698841.
Vancouver
1.Barış Çelik, Erhan Set. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020 Dec. 1;69(2):1057-69. doi:10.31801/cfsuasmas.698841

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

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