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Abdul-Jabbar, Rifaat. (1400). Caputo definition for finding fractional moments of power law distribution functions. نشریه هنرهای کاربردی, 13(1), 1131-1136. doi: 10.22075/ijnaa.2022.5656
Rifaat Saad Abdul-Jabbar. "Caputo definition for finding fractional moments of power law distribution functions". نشریه هنرهای کاربردی, 13, 1, 1400, 1131-1136. doi: 10.22075/ijnaa.2022.5656
Abdul-Jabbar, Rifaat. (1400). 'Caputo definition for finding fractional moments of power law distribution functions', نشریه هنرهای کاربردی, 13(1), pp. 1131-1136. doi: 10.22075/ijnaa.2022.5656
Abdul-Jabbar, Rifaat. Caputo definition for finding fractional moments of power law distribution functions. نشریه هنرهای کاربردی, 1400; 13(1): 1131-1136. doi: 10.22075/ijnaa.2022.5656

Caputo definition for finding fractional moments of power law distribution functions

International Journal of Nonlinear Analysis and Applications
مقاله 95، دوره 13، شماره 1، خرداد 2022، صفحه 1131-1136    اصل مقاله (331.33 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5656
نویسنده
Rifaat Saad Abdul-Jabbar*
Department of Mathematics, College of Science, University of Anbar, Iraq
تاریخ دریافت: 25 اسفند 1399،  تاریخ بازنگری: 12 اردیبهشت 1400،  تاریخ پذیرش: 09 تیر 1400 
چکیده
In this paper, we propose a modern technique to derive fractional moment by using Caputo definition of fractional derivative.  Such technique represents a modification of fractional moments on a certain type of function which is known by the power law distribution functions.  The results have been obtained show that the obtained fractional moments within such functions have closed form.
کلیدواژه‌ها
Fractional moment؛ Caputo definition؛ Power law distribution functions؛ Fourier transform
مراجع

[1] G. Laue, Remarks on the Relation between Fractional Moments and Fractional Derivatives of Characteristic Functions, J. Appl. Probab. 17(2) (1980) 456–466.
[2] G. Cottone and M. Di Paola, On the use of fractional calculus for the probabilistic characterization of random variables, Probab. Egin. Mech. Phys. A 389 (2010) 909—920.
[3] I.B. Bapna and N. Mathur, Application of Fractional Calculus in Statistics, Int. J. Contemp. Math. Sci. 7(18) (2012) 849–856.
[4] K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order, New York: Academic, 1974.
[5] M. Ganji, N. Eghbali and F. Gharari, Some Fractional Special Functions and Fractional Moments, Gen. Math. Notes 18(2) (2013) 120–127.
[6] K. Singh, R. Saxena and S. Kumar Caputo-base fractional derivative in fractional Fourier transform domain, IEEE J. Emerg. Select Topics in Circ. Syst. 3(3) (2013) 23650151.

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