MATHEMATICA, 60 (83), N o 2, 2018, pp. 166–176 NEW INTEGRAL INEQUALITIES FOR (r, α)-FRACTIONAL MOMENTS OF CONTINUOUS RANDOM VARIABLES MOHAMED HOUAS, ZOUBIR DAHMANI, and MEHMET ZEKI SARIKAYA Abstract. In this paper, we establish new integral inequalities for continuous random variables. By introducing new concepts on fractional moments of con- tinuous random variables, we generalize some interesting results of P. Kumar. Other fractional integral results are also presented. MSC 2010. 26D15, 26A33, 60E15. Key words. Integral inequalities, Riemann-Liouville integral, random variable, fractional dispersion, fractional variance, fractional moment. REFERENCES [1] A.M. Acu, F. Sofonea and C.V. Muraru, Gruss and Ostrowski type inequalities and their applications generalization of Chebyshev inequality, Sci. Stud. Res. Ser. Math. Inform., 23 (2013), 5–14. [2] G.A. Anastassiou, M.R. Hooshmandasl, A. Ghasemi and F. Moftakharzadeh, Mont- gomery identities for fractional integrals and related fractional inequalities, JIPAM, 10 (2009), 1–6. [3] G.A. Anastassiou, Fractional differentiation inequalities, Springer-Verlag, New York, 2009. [4] N.S. Barnett, P. Cerone, S.S. Dragomir and J. Roumeliotis, Some inequalities for the expectation and variance of a random variable whose pdf is n-time differentiable, JIPAM, 1 (2000), 1–29. [5] 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, JIPAM, 2 (2001), 1–18. [6] S. Belarbi and Z. Dahmani, On some new fractional integral inequalities, JIPAM, 10 (2009), 1–12. [7] P.L. Chebyshev, Sur les expressions approximatives des integrales definis par les autres prises entre les memes limite, Proc. Math. Soc. Charkov, 2 (1882), 93–98. [8] Z. Dahmani, New applications of fractional calculus on probabilistic random variables, Acta Math. Univ. Comenian. (N.S.), 86 (2017), 299–307. [9] Z. Dahmani and L. Tabharit, On weighted Gruss type inequalities via fractional integrals, JARPM (IASR), 2 (2010), 31–38. [10] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1 (2010), 51–58. [11] Z. Dahmani, L. Tabharit and S. Taf, New generalisations of Gruss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2 (2010), 93–99. [12] Z. Dahmani, Fractional integral inequalities for continuous random variables, Malaya J. Mat., 2 (2014), 172–179. DOI: 10.24193/mathcluj.2018.2.08