15
Views
1
CrossRef citations to date
0
Altmetric
Articles

Pre-Grüss inequality involving conformable fractional integrals and its applications for random variables

&
Pages 757-771 | Received 01 Oct 2018, Published online: 17 Nov 2019

References

  • T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics 279 57–66 (2015). doi: 10.1016/j.cam.2014.10.016
  • T. Abdeljawad, M. A. Horani, R. Khalil, Conformable fractional semigroup operators, Journal of Semigroup Theory and Applications, vol. 2015 Article ID. 7 (2015).
  • M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13(3), 177-183 (2014).
  • M. Abu Hammad, R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13(3), 177-183 (2014).
  • D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, to appear.
  • N. S. Barnett, P. Cerone, S. S. Dragomir and J. Roumeliotis, Some inequalities for the dispersion of a random variable whose pdf is defined on a finite interval, J. Ineq. Pure Appl. Math, 2 (1) (2001).
  • N. S. Barnett and S. S. Dragomir, Some elemantary inequalities for the expectation and variance of a random variable whose pdf is defined on a finite interval, RGMIA Res. Rep. Coll., 2(7), Article 12.
  • N. S. Barnett, S. S. Dragomir and R. P. Agarwal, Some inequalities for probability, evpectation, and variance of random variables defined over a finite interval, Computer and Math. with Appl., 43, 1319-1357 (2002). doi: 10.1016/S0898-1221(02)00103-7
  • N. S. Barnett and S.S. Dragomir, Some inequalities for random variables whose probability density functions are bounded using a pre-Grüss inequality, Kyongpook Mathematical Journal, 40 (2), 11 pp (2000).
  • P. Cerone and S. S. Dragomir, Three Point Quadrature Rules Involving, at Most, a First Derivative, RGMIA Res. Rep. Coll., 4, 2, Article 8 (1999).
  • S. S. Dragomir and I. Fedotov, An inequality of Grüss type for Riemann-Stieltjes integral and applications for special means, Tamkang J. of Math., 29(4), 287-292, (1998).
  • S. S. Dragomir, Some integral inequalities of Grüss type, Indian J. Pure Appl. Math., 31(4), 397-415, (2000).
  • S. S. Dragomir and S. Wang , An inequality of Ostrowski-Grüss’ type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic. Vol. 33, No. 11, pp. 15-20, (1997). doi: 10.1016/S0898-1221(97)00084-9
  • S. Erden, Weighted inequalities involving conformable integrals and its application for random variable and numerical integration, RGMIA Res. Rep. Coll., 20(2017), Article 64, 12 pp.
  • S. Erden, M. Z. Sar kaya and N. Celik, Some generalized inequalities involving local fractional integrals and its applications for random variables and numerical integration, Journal of Applied Mathematics, Statistics and Informatics, 12 (2), 49-65 (2016).
  • G. Grüss, Über das maximum des absoluten Betrages von , Math. Z., 39, 215-226, 1935. doi: 10.1007/BF01201355
  • M. Houas, Some integral inequalities involving Saigo fractional integral operators, Journal of Interdisciplinary Mathematics, 21:3, 681-694 (2018). doi: 10.1080/09720502.2016.1160573
  • O. S. Iyiola and E. R. Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, (2016). doi: 10.18576/pfda/020204
  • R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264, 65-70 (2014). doi: 10.1016/j.cam.2014.01.002
  • P. Kumar, Moments inequalities of a random variable defined over a finite interval, J. Inequal. Pure and Appl. Math. vol.3, ss.3, article 41, (2002).
  • P. Kumar, Inequalities involving moments of a continuous random variable defined over a finite interval, Computers and Mathematics with Applications 48 257-273 (2004). doi: 10.1016/j.camwa.2003.02.014
  • P. Kumar, Hermite-Hadamard inequalities and their applications in estimating moments, In Inequality Theory and Applications, Volume 2, (Edited by Y.J. Cho, J.K. Kim and S.S. Dragomir), Nova Science, (2003).
  • M. Matić, J. E. Pečarić and N. Ujevicć, On new estimation of the remainder in generalized Taylor’s formula, Math. Ineq. & Appl., 3, 2, 343-361 (1999).
  • D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, (1991).
  • B. G. Pachpatte, On Čebyšev-Grüss type inequalities via Pecaric’s extention of the Montgomery identity, J. Inequal. Pure and Appl. Math. 7(1), Art 108, (2006).
  • K. Qiu and J. R. Wang, A fractional integral identity and its application to fractional Hermite-Hadamard type inequalities, Journal of Interdisciplinary Mathematics, 21:1, 1-16 (2018). doi: 10.1080/09720502.2017.1400795
  • M. Z. Sarikaya,On Fejér type inequalities via fractional integrals, Journal of Interdisciplinary Mathematics, 21:1, 143-155 (2018). doi: 10.1080/09720502.2015.1023545
  • M. Z. Sarikaya, A Note on Grüss type inequalities on time scales, Dynamic Systems and Applications, 17, 663-666 (2008).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.