Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 14 Sayı: 1, 201 - 211, 30.06.2022
https://doi.org/10.47000/tjmcs.816174

Öz

Kaynakça

  • 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.

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

Yıl 2022, Cilt: 14 Sayı: 1, 201 - 211, 30.06.2022
https://doi.org/10.47000/tjmcs.816174

Öz

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.

Kaynakça

  • 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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Seda Kılınç 0000-0002-3258-6240

Hüseyin Yıldırım 0000-0001-8855-9260

Yayımlanma Tarihi 30 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 14 Sayı: 1

Kaynak Göster

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 Kılınç S, Yıldırım H. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. Haziran 2022;14(1):201-211. doi:10.47000/tjmcs.816174
Chicago Kılınç, Seda, ve Hüseyin Yıldırım. “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”. Turkish Journal of Mathematics and Computer Science 14, sy. 1 (Haziran 2022): 201-11. https://doi.org/10.47000/tjmcs.816174.
EndNote Kılınç S, Yıldırım H (01 Haziran 2022) Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. Turkish Journal of Mathematics and Computer Science 14 1 201–211.
IEEE S. Kılınç ve H. Yıldırım, “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”, TJMCS, c. 14, sy. 1, ss. 201–211, 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 (Haziran 2022), 201-211. https://doi.org/10.47000/tjmcs.816174.
JAMA Kılınç S, Yıldırım H. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. 2022;14:201–211.
MLA Kılınç, Seda ve Hüseyin Yıldırım. “Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals”. Turkish Journal of Mathematics and Computer Science, c. 14, sy. 1, 2022, ss. 201-1, doi:10.47000/tjmcs.816174.
Vancouver Kılınç S, Yıldırım H. Grüss Type Integral Inequalities For Generalized $\eta -$ Conformable Fractional Integrals. TJMCS. 2022;14(1):201-1.