The contributions given in this paper are in two aspects. The first is to introduce a novel
random function, which we call the multi-fractional generalized Cauchy (mGC) process. The …

This article suggests the contributions with two highlights. One is to propose a novel model
of sea level fluctuations (sea level for short), which is called the generalized Cauchy (GC) …

This paper gives a novel explanation of the integral equation of Abel's type from the point of
view of Mikusinski's operational calculus. The concept of the inverse of Mikusinski's operator …

In many physical applications the electrons play a relevant role. For example, when a beam
of electrons accelerated to relativistic velocities is used as an active medium to generate …

The long-time limit behavior of the positional distribution for an underdamped Brownian
particle in a fluctuating harmonic potential well, which is simultaneously exposed to an …

This book provides a comprehensive theory of mono-and multi-fractal traffic, including the
basics of long-range dependent time series and 1/f noise, ergodicity and predictability of …

We investigate the fluctuation dynamics of photons generated by spontaneous parametric
down conversion (SPDC) using detrended fluctuation analysis (DFA). SPDC photon pairs …

This article contributes the highlights mainly in two folds. On the one hand, it presents a
formula to compute the upper bound of the variance of the correlation periodogram …

The contributions given in this article are mainly in two folds with regard to the fractional
Gaussian noise of the Weyl type. The first one is to present a complete form of fGn, which is …

The long-time limit behavior of velocity correlation functions (VCFs) for an underdamped
Brownian particle in an oscillatory viscoelastic shear flow is investigated using the …