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FRACTIONAL EULER'S INTEGRAL OF FIRST AND SECOND KINDS. APPLICATION TO FRACTIONAL HERMITE'S POLYNOMIALS AND TO PROBABILITY DENSITY OF FRACTIONAL ORDER  

Jumarie, Guy (Department of Mathematics, University of Quebec at Montreal)
Publication Information
Journal of applied mathematics & informatics / v.28, no.1_2, 2010 , pp. 257-273 More about this Journal
Abstract
One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.
Keywords
Fractional calculus; modified Riemann-Liouville derivative; Fractional Euler's integrals; fractional Hermite's polynomials; Fractional Gaussian probability;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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