Jayme Vaz
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View article: On fractional differential equations, dimensional analysis, and the double gamma function
On fractional differential equations, dimensional analysis, and the double gamma function Open
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these…
View article: Stretched non-local Pearson diffusions
Stretched non-local Pearson diffusions Open
We define a novel class of time changed Pearson diffusions, termed stretched non local Pearson diffusions, where the stochastic time change model has the Kilbas Saigo function as its Laplace transform. Moreover, we introduce a stretched va…
View article: Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes Open
In this article, convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse are generalizations of stable and inverse stable subordinat…
View article: On Fractional Spherically Restricted Hyperbolic Diffusion Random Field
On Fractional Spherically Restricted Hyperbolic Diffusion Random Field Open
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random fiel…
View article: Some comments on integrals involving the Dirac delta function
Some comments on integrals involving the Dirac delta function Open
There are two different but equivalent ways of interpreting the integration of the Dirac delta function within the context of the theory of distributions. We discuss both of them and argue that the least known is the most suitable one for …
View article: On the fractional Kelvin-Voigt oscillator
On the fractional Kelvin-Voigt oscillator Open
In this paper we discuss the model of fractional oscillator where the inertial and restoring force terms maintains their usual expression but the damping term involves a fractional derivative of Caputo type, the so called fractional Kelvin…
View article: Spectral Analysis of Fractional Hyperbolic Diffusion Equations with Random Data
Spectral Analysis of Fractional Hyperbolic Diffusion Equations with Random Data Open
The paper studies the fundamental solutions to fractional in time hyperbolic diffusion equation or telegraph equations and their properties. Then it derives the exact solutions of the fractional hyperbolic diffusion equation with random da…
View article: Abordagens Fracionarias para o Oscilador Harmonico
Abordagens Fracionarias para o Oscilador Harmonico Open
O calculo de ordem nao inteira, apesar de nao ser um assunto recente, vem atraindo crescente atencao ao longo dos anos devido a sua ampla gama de possiveis aplicacoes em problemas de interesse cientifico e tecnologico. Popularmente conheci…
View article: On the mistake in defining fractional derivative using a non-singular kernel
On the mistake in defining fractional derivative using a non-singular kernel Open
Definitions of fractional derivative of order $α$ ($0 < α\leq 1$) using non-singular kernels have been recently proposed. In this note we show that these definitions cannot be useful in modelling problems with a initial value condition (li…
View article: On the Clifford Algebraic Description of the Geometry of a 3D Euclidean Space
On the Clifford Algebraic Description of the Geometry of a 3D Euclidean Space Open
We discuss how transformations in a three dimensional euclidean space can be described in terms of the Clifford algebra $\mathcal{C}\ell_{3,3}$ of the quadratic space $\mathbb{R}^{3,3}$. We show that this algebra describes in a unified way…
View article: Life in the Rindler Reference Frame: Does an Uniformly Accelerated Charge Radiates? Is there a Bell `Paradox'? Is Unruh Effect Real?
Life in the Rindler Reference Frame: Does an Uniformly Accelerated Charge Radiates? Is there a Bell `Paradox'? Is Unruh Effect Real? Open
The determination of the electromagnetic field generated by a charge in hyperbolic motion is a classical problem for which the majority view is that the Liénard-Wiechert solution which implies that the charge radiates) is the correct one. …
View article: The Clifford algebra of physical space and Dirac theory
The Clifford algebra of physical space and Dirac theory Open
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