International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Some estimations on continuous random variables involving fractional calculus

  • Zoubir Dahmani
  • Amina Khameli
  • Mohamed Bezziou
  • Mehmet Zeki Sarikaya1*
  1. Düzce University

* Corresponding author

Abstract

Using fractional calculus, new fractional bounds estimating the w- weighted expectation, the w- weighted variance and the w-weighted moment of continuous random variables are obtained. Some recent results on classical bounds estimations are generalized.

How to Cite

Z. Dahmani, A. Khameli, M. Bezziou, M. Z. Sarikaya, Some estimations on continuous random variables involving fractional calculus, Int. J. Anal. Appl. 15 (2017), 8–17.

BibTeX
@article{Dahmani2017,
  author  = {Dahmani, Zoubir and Khameli, Amina and Bezziou, Mohamed and Sarikaya, Mehmet Zeki},
  title   = {Some estimations on continuous random variables involving fractional calculus},
  journal = {Int. J. Anal. Appl.},
  volume  = {15},
  year    = {2017},
  pages   = {8--17},
  doi     = {}
}

References

  • [1] S. Belarbi, Z. Dahmani: On some new fractional integral inequalities. J. Inequal. Pure Appl. Math, 10(3) (2009), 1-12.
  • [2] N.S. Barnett, P. Cerone, S.S. Dragomir, J. Roumeliotis: Some inequalities for the expectation and variance of a random variable whose PDF is n-time diferentiable. J. Inequal. Pure Appl. Math., 1(21) (2000), 1-29.
  • [3] N.S. Barnett, P. Cerone, S.S. Dragomir and J. Roumeliotis: Some inequal-ities for the dispersion of a random variable whose PDF is defined on a finite interval. J. Inequal. Pure Appl. Math., 2(1) (2001), 1-18.
  • [4] Z. Dahmani: Fractional integral inequalities for continuous random variables. Malaya J. Mat., 2(2) (2014), 172-179.
  • [5] Z. Dahmani: New inequalities in fractional integrals. Int. J. Nonlinear Sci., 9(4) (2010), 493-497.
  • [6] Z. Dahmani: On Minkowski and Hermite-Hadamad integral inequalities via fractional integration. Ann. Funct. Anal., 1 (1) (2010), 51-58.
  • [7] Z. Dahmani: New applications of fractional calculus on probabilistic random variables. Acta Math. Univ. Commen., 86 (2) (2017), 299-307.
  • [8] Z. Dahmani, L. Tabharit: On weighted Gruss type inequalities via fractional integrals. J. Adv. Res. Pure Math., 2(4) (2010), 31-38.
  • [9] Z. Dahmani, A.E. Bouziane, M. Houas, M.Z. Sarikaya: New w-weighted concepts for continuous random variables with applications. Note Di Math., In press.
  • [10] R. Gorenflo, F. Mainardi: Fractional calculus: integral and diferential equations of fractional order. Springer Verlag, Wien, (1997), 223-276.
  • [11] P. Kumar: Moment inequalities of a random variable defined over a finite interval. J. Inequal. Pure Appl. Math., 3 (3)(2002), Art. ID 41.
  • [12] P. Kumar: Inequalities involving moments of a continuous random variable defined over a finite interval. Comput. Math. Appl., 48 (2004), 257-273.
  • [13] M. Niezgoda: New bounds for moments of continuous random varialbes, Comput. Math. Appl., 60 (12) (2010), 3130-3138.
  • [14] M.Z. Sarikaya, H. Yaldiz: New generalization fractional inequalities ofOstrowski-Gruss type. Lobachevskii J. Math., 34 (4) (2013), 326-331.
  • [15] M.Z. Sarikaya, H. Yaldiz and N. Basak: New fractional inequalities of Ostrowski-Gruss type. Le Matematiche, 69 (1) (2014), 227-235.
  • [16] R. Sharma, S. Devi, G. Kapoor, S. Ram, N.S. Barnett: A brief note on some bounds connecting lower order moments for random variables defined on a finite interval. Int. J. Theor. Appl. Sci., 1(2), (2009), 83-85.