Results 11 to 20 of about 69 (56)
A Class of Integral Operators and Bessel Plancherel Transform on Lα2
Journal of Function Spaces, Volume 2012, Issue 1, 2012., 2012 For the relation between Bessel Plancherel transform and a wide class of integral operators we establish some results generalizing the corresponding results for the cosine transform, given by Goldberg (1972) and Titchmarsh (1937). Building on these results we obtain a new properties of certain well‐known integral transforms associated with the ...
M. Dziri, Pankaj Jain
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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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A variant of Cowling–Price's and Miyachi's theorems for the Bessel–Struve transform on ℝd
Journal of Taibah University for Science, 2018 In this paper, we consider the Bessel–Struve transform on $ \mathbb {R}^{d} $ . We establish new versions of Cowling–Price's and Miyachi's theorems for the Bessel–Struve transform on $ \mathbb {R}^{d} $ .
Hatem Mejjaoli, Khalifa Trimèche
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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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Contact problem of torsion of a multilayer base with elastic connections between layers
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 Torsion of a multilayer base with elastic connections between layers by cylindrical punch with a flat sole was considered. The Hankel integral transform of the first order and the method of the compliance functions were used.
Nina N Antonenko, Igor G Velichko
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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.
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Operational Calculus for the general fractional derivatives with the Sonine kernels
, 2021 30 pages.
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General fractional integral operators do not preserve periodicity
Examples and CounterexamplesIf a periodic real function is differentiable, its derivative is also periodic with the same period. The primitive of a periodic function is periodic if the mean value of the function, over a period, is zero.It is well known that the fractional integral ...
Hamza Al-Shdaifat +2 more
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Fractional Calculus and Applied AnalysisAbstractThe 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.
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