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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
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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
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Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 131-145, 1999., 1999 The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long‐time asymptotics is calculated explicitly and a uniform in space estimate of the residual ...
Vladimir V. Varlamov
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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
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Tracer diffusion coefficients in a moderately dense granular suspension. Stability analysis and thermal diffusion segregation [PDF]
, 2023 The diffusion transport coefficients of a binary granular suspension where one of the components is present in tracer concentration are determined from the (inelastic) Enskog kinetic equation.
Garzó, Vicente +1 more
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Sonine integral equations [PDF]
, 2006 As equações integrais de Sonine são equações de primeira espécie, de Volterra, Kfp =f , com núcleo às diferenças, tais que existe um núcleo associado ao núcleo original de modo que sejam ambos divisores da unidade para a convolução.
Cardoso, Rogério Pereira
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On a q-Dunkl sonine transform [PDF]
, 2013 In this paper, we introduce and study the q-Dunkl Sonine transform and we establish a Plancherel formula for its dual.
Bettaieb, Rym Hasna +2 more
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On generalized fractional differential equation with Sonine kernel on a function space
Partial Differential Equations in Applied MathematicsSonine kernel is a special type of the general kernels, satisfying some integrability and monotonicity conditions and properties. Sonine kernels generate some convolution polynomials (power functions) used in the construction of the general fractional ...
McSylvester Ejighikeme Omaba
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Beta distributions and Sonine integrals for Bessel functions on symmetric cones [PDF]
, 2018 There exist several multivariate extensions of the classical Sonine integral representation for Bessel functions of some index μ + v with respect to such functions of lower index μ.
Voit, Michael, Rösler, Margit
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Variable-order fractional calculus: A change of perspective [PDF]
, 2021 Several approaches to the formulation of a fractional theory of calculus of “variable order” have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an alternative view on
Garrappa R. +8 more
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