New Applications of Fractional Calculus on Probabilistic Random Variables
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Abstract
New results and new applications of fractional calculus for continuous random variables are presented. Some classical integral results are also generalized. On the other hand, some results (corollaries) on the paper [Fractional integral inequalities for continuous random variables, Malaya J. Mat. 2(2), (2014), 172-179] are corrected.
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How to Cite
Dahmani, Z.
(2017).
New Applications of Fractional Calculus on Probabilistic Random Variables.
Acta Mathematica Universitatis Comenianae, 86(2), 299-307.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/466/473
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References
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[6] Z. Dahmani, L. Tabharit: On weighted Gruss type inequalities via fractional integrals, JARPM, Journal of Advanced Research in Pure Mathematics, Vol. 2 Iss. 4 (2010), 31-38.
[7] Z. Dahmani: On Minkowski and Hermite-Hadamad integral inequalities via fractional integration, Ann. Funct. Anal., Vol. 1 Iss. 1 (2010), 51-58
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[12] Y. Miao, G. Yang: A note on the upper bounds for the dispersion, J. Inequal. Pure Appl. Math., Vol. 8 Iss. 3 Art. 83 (2007), 1-13.
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[14] M. Niezgoda: New bounds for moments of continuous random varialbes, Comput. Math. Appl., Vol. 60 Iss. 12, (2010), 3130-3138.
[15] F. Qi, A.J. Li, W.Z. Zhao, D.W. Niu, J. Cao: Extensions of several integral inequalities, J. Inequal. Pure Appl. Math., Vol. 7 Iss. 3 Art. 107, (2006), 1-6.
[16] F. Qi: Several integral inequalities, J. Inequal. Pure Appl. Math., Vol. 1 Iss. 2 Art. 19 (2000), 1-9.
[17] M.Z. Sarikaya, N. Aktan, H. Yildirim: On weighted Chebyshev-Gruss like inequalities on time scales, J. Math. Inequal., Vol. 2 Iss. 2 ( 2008), 185-195.
[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 differentiable, J. Inequal. Pure Appl. Math., Vol. 1 Art. 21 (2000), 1-29
[3] 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. Inequal. Pure Appl. Math., Vol. 2 Iss. 1 Art. 1 (2001),
1-18.
[4] S. Belarbi, Z. Dahmani: On some new fractional integral inequalities, J. Inequal. Pure Appl. Math., Vol. 10 Iss. 3 Art. 86 (2009), 1-12.
[5] Z. Dahmani: New inequalities in fractional integrals, International Journal of Nonlinear Sciences, Vol. 9 Iss. 4 (2010), 493-497.
[6] Z. Dahmani, L. Tabharit: On weighted Gruss type inequalities via fractional integrals, JARPM, Journal of Advanced Research in Pure Mathematics, Vol. 2 Iss. 4 (2010), 31-38.
[7] Z. Dahmani: On Minkowski and Hermite-Hadamad integral inequalities via fractional integration, Ann. Funct. Anal., Vol. 1 Iss. 1 (2010), 51-58
[8] Z. Dahmani: Fractional integral inequalities for continuous random variables, Malaya J. Mat. 2(2)(2014) 172-179.
[9] R. Goreno, F. Mainardi: Fractional calculus: integral and differential equations of fractional order, Springer Verlag, Wien, (1997), 223-276.
[10] P. Kumar: Moment inequalities of a random variable defined over a finite interval, J. Inequal. Pure Appl. Math., Vol. 3 Iss. 3, Art. 41 (2002), 1-24.
[11] P. Kumar: Inequalities involving moments of a continuous random variable defined over a finite interval, Computers and Mathematics with Applications, 48 (2004), 257-273
[12] Y. Miao, G. Yang: A note on the upper bounds for the dispersion, J. Inequal. Pure Appl. Math., Vol. 8 Iss. 3 Art. 83 (2007), 1-13.
[13] T.F. Mori: Sharp inequalities between centered moments, J. Math. Annal. Appl., Vol. 10 Iss. 4 Art. 99 (2009), 1-19.
[14] M. Niezgoda: New bounds for moments of continuous random varialbes, Comput. Math. Appl., Vol. 60 Iss. 12, (2010), 3130-3138.
[15] F. Qi, A.J. Li, W.Z. Zhao, D.W. Niu, J. Cao: Extensions of several integral inequalities, J. Inequal. Pure Appl. Math., Vol. 7 Iss. 3 Art. 107, (2006), 1-6.
[16] F. Qi: Several integral inequalities, J. Inequal. Pure Appl. Math., Vol. 1 Iss. 2 Art. 19 (2000), 1-9.
[17] M.Z. Sarikaya, N. Aktan, H. Yildirim: On weighted Chebyshev-Gruss like inequalities on time scales, J. Math. Inequal., Vol. 2 Iss. 2 ( 2008), 185-195.