Some estimations on continuous random variables for (k, s) −fractional integral operators

$Some estimations on continuous random variables for (k, s) −fractional integral operators Cover$

Some estimations on continuous random variables for (k, s) −fractional integral operators

Moroccan Journal of Pure and Applied Analysis

Volume 6 (2020): Issue 1 (June 2020)

By:

Mohamed Houas

Open Access

|May 2020

References

[1] A. Akkurt, Z. Kaçar, H. Yildirim. Generalized fractional integral inequalities for continuous random variables. Journal of Probability and Statistics. Vol 2015. Article ID 958980, (2015), 1-7.<a href="https://doi.org/10.1155/2015/958980" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1155/2015/958980</a>
Search in Google Scholar Back to article
[2] 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. J. Inequal. Pure Appl. Math. 1, (2000), 1-29.
Search in Google Scholar Back to article
[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. 2, (2001), 1-18.
Search in Google Scholar Back to article
[4] T. Cacoullos and V. Papathanasiou. On upper boundsfor the variance of functions of random varialbes. Statist. Probab. Lett. 7 (1985), 175-184.<a href="https://doi.org/10.1016/0167-7152(85)90014-8" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/0167-7152(85)90014-8</a>
Search in Google Scholar Back to article
[5] T. Cacoullos and V. Papathanasiou. Caracterizations of distributuons by variance bounds. Math. Statist. 4 (1989), 351-356.<a href="https://doi.org/10.1016/0167-7152(89)90050-3" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/0167-7152(89)90050-3</a>
Search in Google Scholar Back to article
[6] Z. Dahmani. Fractional integral inequalities for continuous random variables. Malaya J. Math. 2(2), (2014), 172-179.
Search in Google Scholar Back to article
[7] Z. Dahmani. New applications of fractional calculus on probabilistic random variables. Acta Math. Univ. Comenianae. 86(2) (2016), 1-9.
Search in Google Scholar Back to article
[8] Z. Dahmani, A. Khameli, M. bezziou and M.Z. Sarikaya. Some estimations on continuous random variables involving fractional calculus. International Journal of Analysis and Applications. 15(1), (2017), 8-17.
Search in Google Scholar Back to article
[9] Z. Dahmani, A.E. Bouziane, M. Houas and M.Z. Sarikaya. New W−weighted concepts for continuous random variables with applications. Note di. Mat., 37 (2017), 23-40.
Search in Google Scholar Back to article
[10] M. Houas, Z. Dahmani and M. Z. Sarikaya. New integral inequalities for (r, α) −fractional moments of continuous random variables. Mathematica. 60 (2), (2018), 166-176.<a href="https://doi.org/10.24193/mathcluj.2018.2.08" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.24193/mathcluj.2018.2.08</a>
Search in Google Scholar Back to article
[11] M. Houas, Z. Dahmani. Random variable inequalities involving (k, s)−integration. Malaya J. Math. 5(4), (2017), 641-646.<a href="https://doi.org/10.26637/MJM0504/0005" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.26637/MJM0504/0005</a>
Search in Google Scholar Back to article
[12] M. Houas. Some inequalities for k−fractional continuous random variables. J. Advan. Res. In Dynamical and Control Systems. 7(4) (2015), 43-50.
Search in Google Scholar Back to article
[13] P. Kumar. Inequalities involving moments of a continuous random variable defined over a finite interval. Comput. Math. Appl. 48, (2004), 257-273.<a href="https://doi.org/10.1016/j.camwa.2003.02.014" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.camwa.2003.02.014</a>
Search in Google Scholar Back to article
[14] P. Kumar. The Ostrowski type moment integral inequalities and moment-bounds for continuous random variables. Comput. Math. Appl. 49 (2005), 1929-1940.<a href="https://doi.org/10.1016/j.camwa.2003.11.002" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.camwa.2003.11.002</a>
Search in Google Scholar Back to article
[15] O. M. Khellaf, V.L. Chinchane. Continuous random variables with Hadamard fractional integral. Tamkang J. Math. 50(1), (2019), 103-109.<a href="https://doi.org/10.5556/j.tkjm.50.2019.2763" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.5556/j.tkjm.50.2019.2763</a>
Search in Google Scholar Back to article
[16] M. Niezgoda. New bounds for moments of continuous random varialbes. Comput. Math. Appl., 60 (12) (2010), 3130-3138.<a href="https://doi.org/10.1016/j.camwa.2010.10.018" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.1016/j.camwa.2010.10.018</a>
Search in Google Scholar Back to article
[17] M. Z. Sarikaya, Z. Dahmani, M.E. Kiris and F. Ahmad. (k, s)−Riemann-Liouville fractional integral and applications. Hacet J. Math. Stat. 45(1) (2016), 1-13.<a href="https://doi.org/10.15672/HJMS.20164512484" target="_blank" rel="noopener noreferrer" class="text-signal-blue hover:underline">10.15672/HJMS.20164512484</a>
Search in Google Scholar Back to article
[18] M. Z. Sarikaya and A. Karaca. On the k−Riemann-Liouville fractional integral and applications. International Journal of Statistics and Mathematics. 1(3) (2014), 033-043.
Search in Google Scholar Back to article
[19] M. Tomar, S. Maden, E. Set. (k, s)−Riemann–Liouville fractional integral inequalities for continuous random variables. Arab. J. Math. 6 (2017), 55-63.
Search in Google Scholar Back to article