A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included Blachman-Stam type inequalities. These inequalities relate the fractional Fisher information of the sum of n independent random variables to the information co...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

The calculation of a statistical measure of complexity and the Fisher-Shannon information in nuclei is carried out in this work. We use the nuclear shell model in order to obtain the fractional occupation probabilities of nuclear orbitals. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the number of nucleons is observed. The shell structur...

Maddala and Wu (1999) proposed a simple panel unit test using a Fisher type test. We propose using Percival and Walden (2006) approximate maximum likelihood estimator of the fractional integration order with a Fisher type test to create a simple panel fractional integration order test. By combining the estimator and the test with a wavestrap method to obtain critical values, we allow for cross-...

We study an extension of the classical Fisher-KPP equation to stratified groups. show positivity, boundedness, asymptotic time-behavior, and blow-up in finite time solutions. These results are also discussed for (time-fractional) by means Caputo time-fractional derivative.

We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplac...