International Journal of Nonlinear Analysis and Applications
Caputo definition for finding fractional moments of power law distribution functions
Document Type : Research Paper
Author
Department of Mathematics, College of Science, University of Anbar, Iraq
Abstract
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.
Keywords
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[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.
[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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Volume 13, Issue 1
March 2022Pages 1131-1136
- Receive Date: 15 March 2021
- Revise Date: 02 May 2021
- Accept Date: 30 June 2021