Research Article

Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals

Volume: 14 Number: 1 June 30, 2022
EN

Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals

Abstract

Our aim in this paper is to establish new $\eta -$conformable fractional integral. For this purpose new inequalities are obtained by using generalized $\eta -$conformable fractional integral with the help of Grüss type integrals. The inequalities that exist in the literature are obtained in case of some special choices, which shows that the inequality we achieve is a more general inequality.

Keywords

References

  1. Budak, H., Sarikaya, M.Z., An inequality of Ostrowski-Grüss type for double integrals, Stud. Univ. Babes-Bolyai Math, 62(2017), 163-173.
  2. Budak, H., Sarikaya, M.Z., On weighted Grüss type inequalities for double integrals, Commun. Fac. Sci. Univ. Ank. Series A1, 66(2)(2017), 53-61.
  3. Çelik, B., Set, E., Akdemir, A.O., Mixed conformable fractional grüss type inequalities, www.researchgate.net, (2019).
  4. Dragomir, S.S., Some integral inequalities of Grüss type, Indian Journal of Pure and Applied Mathematics, 31(4)(2002), 397-415.
  5. Dragomir, S.S., A companion of the Grüüss inequality and applications, Applied Mathematics Letters, 17(4)(2004), 429-435.
  6. Grüss, G., Uber das maximum des absoluten Betrages von \begin{equation*} \frac{1}{b-a}\int\nolimits_{a}^{b}f(x)g(x)dx-\frac{1}{(b-a)^{2}}% \int\nolimits_{a}^{b}f(x)dx\int\nolimits_{a}^{b}g(x)dx \end{equation*} Mathematische Zeitschrift, 39(1935), 215-226.
  7. Jarad, F., Ugurlu, E., Abdeljawad, T., Baleanu, D. , On a new class of fractional operators, Advances in Difference Equations, 247(2017).
  8. Jarad, F., Abdeljawad, T., Generalized fractional derivatives and Laplace transforms, Discrete and Continuous Dynamical Systems: Series S, 13(3)(2020), 709-722.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

June 30, 2022

Submission Date

October 25, 2020

Acceptance Date

July 26, 2021

Published in Issue

Year 2022 Volume: 14 Number: 1

APA
Kılınç, S., & Yıldırım, H. (2022). Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. Turkish Journal of Mathematics and Computer Science, 14(1), 201-211. https://doi.org/10.47000/tjmcs.816174
AMA
1.Kılınç S, Yıldırım H. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. 2022;14(1):201-211. doi:10.47000/tjmcs.816174
Chicago
Kılınç, Seda, and Hüseyin Yıldırım. 2022. “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”. Turkish Journal of Mathematics and Computer Science 14 (1): 201-11. https://doi.org/10.47000/tjmcs.816174.
EndNote
Kılınç S, Yıldırım H (June 1, 2022) Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. Turkish Journal of Mathematics and Computer Science 14 1 201–211.
IEEE
[1]S. Kılınç and H. Yıldırım, “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”, TJMCS, vol. 14, no. 1, pp. 201–211, June 2022, doi: 10.47000/tjmcs.816174.
ISNAD
Kılınç, Seda - Yıldırım, Hüseyin. “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”. Turkish Journal of Mathematics and Computer Science 14/1 (June 1, 2022): 201-211. https://doi.org/10.47000/tjmcs.816174.
JAMA
1.Kılınç S, Yıldırım H. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. 2022;14:201–211.
MLA
Kılınç, Seda, and Hüseyin Yıldırım. “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 1, June 2022, pp. 201-1, doi:10.47000/tjmcs.816174.
Vancouver
1.Seda Kılınç, Hüseyin Yıldırım. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. 2022 Jun. 1;14(1):201-1. doi:10.47000/tjmcs.816174

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