• GENERALIZED FOURIER TRANSFORM FOR THE GENERATION OF COMPLEX FRACTIONAL MOMENTS

Abstract

Fourier transform of fractional order using the Mittag-Leffler-type function  and its complex type, was introduced together with its inversion formula. The obtained transform provided a suitable generalization of the characteristic function of random variables. It was shown that complex fractional moments which are complex moments of order nq^th of a certain distribution, are equivalent to Caputa fractional derivation of generalized characteristic function (GCF) in origin, n being a positive integer and 0 < q ≤ 1. The case q=1 was reduced to the complex moments. Finally, after introducing fractional factorial moments of a positive random variable, we presented the relationship between integer moments, fractional moments (FMs) and fractional factorial moments (FFMs) of a positive random variable.