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

Year 2022, Volume: 14 Issue: 1, 201 - 211, 30.06.2022

Seda Kılınç , Hüseyin Yıldırım

https://doi.org/10.47000/tjmcs.816174

Cited By: 1

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

Fractional integral, Grüss inequality, Riemann-Liouville fractional integral

References

• Budak, H., Sarikaya, M.Z., An inequality of Ostrowski-Grüss type for double integrals, Stud. Univ. Babes-Bolyai Math, 62(2017), 163-173.
• 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.
• Çelik, B., Set, E., Akdemir, A.O., Mixed conformable fractional grüss type inequalities, www.researchgate.net, (2019).
• Dragomir, S.S., Some integral inequalities of Grüss type, Indian Journal of Pure and Applied Mathematics, 31(4)(2002), 397-415.
• Dragomir, S.S., A companion of the Grüüss inequality and applications, Applied Mathematics Letters, 17(4)(2004), 429-435.
• 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.
• Jarad, F., Ugurlu, E., Abdeljawad, T., Baleanu, D. , On a new class of fractional operators, Advances in Difference Equations, 247(2017).
• Jarad, F., Abdeljawad, T., Generalized fractional derivatives and Laplace transforms, Discrete and Continuous Dynamical Systems: Series S, 13(3)(2020), 709-722.
• Kaçar, E., Kaçar, Z., Yıldırım, H., Integral inequalities for Riemann-Liouville fractional integrals of a function with respect to another function, Iranian Journal of Mathematical Sciences and Informatics, 13(1)(2018), 1-13.
• Kilbas, A., Srivastava, M.H., Trujillo, J.J., Theory and Application of Fractional Differential Equations, North Holland Mathematics Studies, 2006.
• Tariboon, J., Ntouyas, S.K., Sudsutad, W., Some new Riemann-Liouville fractional integral inequalities, Int. J. Math. Math. Sci., (2014), Article ID 869434, 1-6.