Now, evaluating the Mellin transform
of [t.sup.[??]+vn-1] using formula given by Mathai et al.
Gong, "Novel optical image encryption scheme based on fractional Mellin transform
," Optics Communications, vol.
The Mellin transform
of the function f is defined by
Bayram and others used Fourier Mellin Transform
to represent the blocks .
In the present paper we point out the deep connections between of our iterated operators and the generalized Hadamard integrals, introduced firstly in , and widely used in Mellin analysis, especially in fractional calculus in Mellin transform
setting (see e.g.
Using the Mellin transform
, we find asymptotic expressions for these averages.
Alternately, characteristic function of the second kind, derived using Mellin transform
, can be used to find the stochastic properties of nonnegative random variables .
Compared to most transform-based techniques which are linear in nature, the fractional Mellin transform
(FrMT) is a nonlinear transform and could potentially provide security against most known attacks [17, 31].
Furthermore, using the second-kind statistics theory developed by Nicolas , which relies on the Mellin transform
, i.e., "method-of-log-cumulants" (MoLC), we derive the parameter estimators of the new distribution model.
The leading order term is expressed in the form of inverse Mellin transform
. The transformant crucially depends on the parameter [chi] = k[[[rho].sup.t].sup.3/2] [[rho].sup.-1/2] which characterizes the rate of elongation of the body.
In some cases, there are some methods to solve fractional partial differential equations and get the analytical solutions , such as Fourier transform methods, Laplace transform methods, Mellin transform
methods, the method of images, and the method of separation of variables.
and Brahim K.: The Mellin transform
in quantum calculus.