Results 11 to 20 of about 265 (83)

The dual integral equation method in hydromechanical systems

Journal of Applied Mathematics, Volume 2004, Issue 6, Page 447-460, 2004., 2004
Some hydromechanical systems are investigated by applying the dual integral equation method. In developing this method we suggest from elementary appropriate solutions of Laplace′s equation, in the domain under consideration, the introduction of a potential function which provides useful combinations in cylindrical and spherical coordinates systems ...
N. I. Kavallaris, V. Zisis
wiley   +1 more source

Sonine Transform Associated to the Dunkl Kernel on the Real Line [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We consider the Dunkl intertwining operator $V_ $ and its dual ${}^tV_ $, we define and study the Dunkl Sonine operator and its dual on $\mathbb{R}$. Next, we introduce complex powers of the Dunkl Laplacian $ _ $ and establish inversion formulas for the Dunkl Sonine operator $S_{ , }$ and its dual ${}^tS_{ , }$.
openaire   +5 more sources

Integral equations of the first kind of Sonine type

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 57, Page 3609-3632, 2003., 2003
A Volterra integral equation of the first kind Kφ(x):≡∫−∞xk(x−t)φ(t)dt=f(x) with a locally integrable kernel k(x)∈L1loc(ℝ+1) is called Sonine equation if there exists another locally integrable kernel ℓ(x) such that ∫0xk(x−t)ℓ(t)dt≡1 (locally integrable divisors of the unit, with respect to the operation of convolution). The formal inversion φ(x)=(d/dx)
Stefan G. Samko, Rogério P. Cardoso
wiley   +1 more source

A note on Bessel function dual integral equation with weight function

International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 3, Page 543-549, 1988., 1987
An elementary procedure based on Sonine′s integrals has been used to reduce dual integral equations with Bessel functions of different orders as kernels and an arbitrary weight function to a Fredholm integral equation of the second kind. The result obtained here encompasses many results concerning dual integral equations with Bessel functions as ...
B. N. Mandal
wiley   +1 more source

The action of Volterra integral operators with highly singular kernels on H\"older continuous, Lebesgue and Sobolev functions

, 2017
For kernels $\nu$ which are positive and integrable we show that the operator $g\mapsto J_\nu g=\int_0^x \nu(x-s)g(s)ds$ on a finite time interval enjoys a regularizing effect when applied to H\"older continuous and Lebesgue functions and a "contractive"
Adami, Adami, Adami, Adams, Alberto Fiorenza, Albeverio, Cacciapuoti, Cacciapuoti, Cardoso, Carlone, Carlone, Cruz-Uribe, Demengel, Di Nezza, Erdélyi, Fiorenza, Fiorenza, Fiorenza, Garrappa, Gorenflo, Hardy, Hardy, Hrusa, Krasnosel'skiĭ, Kufner, König, König, Ladopoulos, Lorenzo Tentarelli, Maligranda, O'Neil, Okikiolu, Raffaele Carlone, Rao, Samko, Samko, Samko, Sharpley, Sonine, Tarasov   +39 more
core   +1 more source

Operational Calculus for the general fractional derivatives with the Sonine kernels

, 2021
30 pages.
openaire   +2 more sources

General Fractional Calculus, Evolution Equations, and Renewal Processes

, 2011
We develop a kind of fractional calculus and theory of relaxation and diffusion equations associated with operators in the time variable, of the form $(Du)(t)=\frac{d}{dt}\int\limits_0^tk(t-\tau)u(\tau)\,d\tau -k(t)u(0)$ where $k$ is a nonnegative ...
Kochubei, Anatoly N.
core   +1 more source

Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory

, 2011
The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of ...
Garcia-Colin, L. S., Moratto, Valdemar
core   +1 more source

Uniformly Continuous Generalized Sliding Mode Control

Mathematics
This paper explores a general class of singular kernels with the objective of designing new families of uniformly continuous sliding mode controllers. The proposed controller results from filtering a discontinuous switching function by means of a Sonine ...
Aldo Jonathan Muñoz-Vázquez, Guillermo Fernández-Anaya   +1 more
doaj   +1 more source

Linear hydrodynamics for driven granular gases

, 2012
We study the dynamics of a granular gas heated by the stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit.
de Soria, M. I. Garcia, Maynar, P., Trizac, E.   +2 more
core   +3 more sources