Results 1 to 10 of about 74,628 (79)

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

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

Symmetrical Sonin kernels in terms of the hypergeometric functions

, 2023
In this paper, we introduce a new class of the kernels of the integral transforms of the Laplace convolution type that we call symmetrical Sonin kernels. For a symmetrical Sonin kernel given in terms of some elementary or special functions, its associated kernel has the same form with possibly different parameter values.
openaire   +2 more sources

Operational Calculus for the general fractional derivatives with the Sonine kernels

, 2021
30 pages.
openaire   +2 more sources

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

Searching for Sonin kernels

Fractional Calculus and Applied Analysis
AbstractThe causal shift-invariant convolution is studied from the point of view of inversion. Abel’s algorithm, used in the tautochrone problem, is considered and Sonin’s existence condition is deduced. To generate pairs of functions verifying Sonin’s condition, the class of Mittag-Leffler type functions is used.
openaire   +2 more sources

Anomalous Diffusion Models Involving Regularized General Fractional Derivatives with Sonin Kernels

Fractal and Fractional
In this paper, we introduce a general fractional master equation involving regularized general fractional derivatives with Sonin kernels, and we discuss its physical characteristics and mathematical properties. First, we show that this master equation can be embedded into the framework of continuous time random walks, and we derive an explicit formula ...
Maryam Alkandari, Dimitri Loutchko, Yuri Luchko   +2 more
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On the Rigorous Correspondence Between Operator Fractional Powers and Fractional Derivatives via the Sonine Kernel

Fractal and Fractional
Traditional operational calculus, while intuitive and effective in addressing problems in physical fractal spaces, often lacks the rigorous mathematical foundation needed for fractional operations, sometimes resulting in inconsistent outcomes. To address these challenges, we have developed a universal framework for defining the fractional calculus ...
Zelin Liu, Xiaobin Yu, Yajun Yin
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On Symmetrical Sonin Kernels in Terms of Hypergeometric-Type Functions

Mathematics
In this paper, a new class of kernels of integral transforms of the Laplace convolution type that we named symmetrical Sonin kernels is introduced and investigated. For a symmetrical Sonin kernel given in terms of elementary or special functions, its associated kernel has the same form with possibly different parameter values. In the paper, several new
openaire   +2 more sources