Analytical solutions for Navier-Stokes equations with ψ\psi-Caputo fractional derivative

This work aims to use the homotopy analysis method to obtain analytical solutions of linear time-fractional Navier-Stokes equations with cylindrical coordinates and of a system of nonlinear time-fractional Navier-Stokes equations with Cartesian coordinates. These equations are described in the $\psi$-Caputo time-fractional derivative. The solutions obtained for time-fractional Navier-Stokes equations are graphically presented.Comment: 17 pages, 8 figures. arXiv admin note: text overlap with arXiv:2004.0236

Hilfer-Katugampola fractional derivative

We propose a new fractional derivative, the Hilfer-Katugampola fractional derivative. Motivated by the Hilfer derivative this formulation interpolates the well-known fractional derivatives of Hilfer, Hilfer-Hadamard, Riemann-Liouville, Hadamard, Caputo, Caputo-Hadamard, Liouville, Weyl, generalized and Caputo-type. As an application, we consider a nonlinear fractional differential equation with an initial condition using this new formulation. We show that this equation is equivalent to a Volterra integral equation and demonstrate the existence and uniqueness of solution to the nonlinear initial value problem.Comment: 21 page

Wavelet Analysis as an Information Processing Technique

A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.Comment: 6 pages, 6 tables, VI International Telecommunications Symposium (ITS2006), September 3-6, Fortaleza, Brazi

Child mortality in Penna ageing model

Assuming the deleterious mutations in the Penna ageing model to affect mainly the young ages, we get an enhanced mortality at very young age, followed by a minimum of the mortality, and then the usual exponential increase of mortality with age.Comment: To pages including one figur

Taylor Series as Wide-sense Biorthogonal Wavelet Decomposition

Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis.Comment: 6 pages, 4 figures. conference: XXII Simposio Brasileiro de Telecomunicacoes, SBrT'05, 2005, Campinas, SP, Brazi

Three-dimensional black holes with quintessence

We study a quintessential black hole solution in three dimensions, with mass and quintessence charge. By exploring the Carter-Penrose diagram, we show the presence of spacelike and lightlike singularities in the metric, given different values for the quintessence parameter, as well as an AdS-like spatial infinity and event horizon encapsulating the singularity. We also study the propagation of scalar and Dirac (Weyl) fields around the black hole solutions with different quintessence charges obtaining the quasinormal spectra for both fields using two different numerical methods with good agreement between the data. In both cases, the presence of quintessence increases the imaginary part of the quasinormal mode, since this is related to the event horizon of the solution, preserving the interpretation of this quantity as relaxation time in the corresponding CFT. We also investigate the behavior of high-temperature scalar field modes, demonstrating the presence of the so-called hydrodynamical limit, differently from the BTZ black hole, for which no such modes exist.Comment: 28 pages, 5 tables, 5 figures. In v2, typos corrected. Appendix added with analytical results. To appear in Physical Review

About the Phasor Pathways in Analogical Amplitude Modulation

The Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard Amplitude Modulation Systems (e.g. A3E, H3E, J3E, C3F). A cornucopia of algebraic curves is then derived assuming a single tone or a double tone modulation signal. The ratio of the frequency of the tone modulator (fm) and carrier frequency (fc) is considered in two distinct cases, namely: fm/fc<1 and fm/fc>=1. The geometric figures are some sort of Lissajours figures. Different shapes appear looking like epicycloids (including cardioids), rhodonea curves, Lemniscates, folium of Descartes or Lam\'e curves. The role played by the modulation index is elucidated in each case.Comment: 10 pages, 15 figures. ISSN 2320-936

On the existence and stability for non-instantaneuos impulsive fractional integrodifferential equation

In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam--Hyers--Rassias stability of the non-instantaneous impulsive integrodifferential equation by means of $\psi$-Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.Comment: 15 page

Gruss-type inequality by mean of a fractional integral

In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with these inequalities and then immediately we enunciate and prove others inequalities associated with these fractional operator.Comment: 16 page

Simple Bit-String Model for Lineage Branching

We introduce a population dynamics model, where individual genomes are represented by bit-strings. Selection is described by death probabilities which depend on these genomes, and new individuals continuously replace the ones that die, keeping the population constant. An offspring has the same genome as its (randomly chosen) parent, except for a small amount of (also random) mutations. Chance may thus generate a newborn with a genome that is better than that of its parent, and the newborn will have a smaller death probability. When this happens, this individual is a would-be founder of a new lineage. A new lineage is considered created if its alive descendence grows above a certain previously defined threshold. The time evolution of populations evolving under these rules is followed by computer simulations and the probability densities of lineage duration and size, among others, are computed. These densities show a scale-free behaviour, in accordance with some conjectures in paleoevolution, and suggesting a simple mechanism as explanation for the ubiquity of these power-laws.Comment: 16 pages biophysics, including 7 figure