In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic ...

Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...

The inverse stable subordinator is the first passage time of a standard stable subordinator with index 0 < β < 1. The probability density of the inverse stable subordinator can be used to solve time-fractional Cauchy problems, where the usual first derivative in time is replaced by a Caputo fractional derivative of order β. If the Cauchyproblemgoverns aMarkov process, then the fractional Cauchy...

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two quadratures. This theoretical result is corroborated by numerical simulations for different shapes of the periodic potential. Normal and fractional spreading process...

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two quadratures. This theoretical result is corroborated by numerical simulations for different shapes of the periodic potential. Normal and fractional spreading processe...

In the framework of cell structure characterization for predictive oncology, we propose in this paper an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical de...

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional ent...

One considers a class of fractional random processes defined as non-random dynamics subject to Gaussian white noises in coarse-grained time, according to Maruyama’s notation. After some prerequisites on modified Riemann-Liouville fractional derivative, fractional Taylor’s series and integration with respect to (dx)α , one displays the main results which are as follows: firstly, a general scheme...

The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigate...

INTRODUCTION Asthma is a chronic respiratory disease characterized by hyper-responsiveness and bronchial inflammation. The bronchial inflammation in these patients can be monitored by measuring the fractional exhaled nitric oxide. This study aims to determine fractional exhaled nitric oxide association with peak expiratory flow and with asthma control inferred by the Global Initiative for Asthm...