Results 11 to 20 of about 696 (148)
Babenko’s Approach to Abel’s Integral Equations [PDF]
Mathematics, 2018 The goal of this paper is to investigate the following Abel’s integral equation of the second kind: y ( t ) + λ Γ ( α ) ∫ 0 t ( t − τ ) α − 1 y ( τ ) d τ = f ( t ) , ( t > 0 ) and its variants by fractional calculus. Applying Babenko’s approach and fractional integrals, we provide a general method for solving Abel’s ...
Chenkuan Li, Kyle Clarkson
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Optimal quadrature formulas in Sobolev space for solving the generalized Abel integral equation [PDF]
E3S Web of ConferencesIn this article, a composite optimal quadrature formula is constructed for an approximate analytical solution of the generalized integral Abel equation in the Sobolev functional space.
Daliyev Bakhtiyor +5 more
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On Solvability of the Sonin–Abel Equation in the Weighted Lebesgue Space
Fractal and Fractional, 2021 In this paper we present a method of studying a convolution operator under the Sonin conditions imposed on the kernel. The particular case of the Sonin kernel is a kernel of the fractional integral Riemman–Liouville operator, other various types of the ...
Maksim V. Kukushkin
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Properties of inversion operator of the Abel matrix equation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 Generalization of integral-differential Riemann-Liouville operator on the matrix order-is reviewed and its properties are studied. Theorem of the composition of operators of the matrix of integration and differentiation can be proved.
Rina R Ismagilova
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On the Solution of Distributional Abel Integral Equation by Distributional Sumudu Transform
International Journal of Mathematics and Mathematical Sciences, 2011 Solution of the Abel integral equation is obtained using the Sumudu transform and further, distributional Sumudu transform, and, distributional Abel equation are established.
Deshna Loonker, P. K. Banerji
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IET Microwaves, Antennas & Propagation, 2021 The transmission of an electromagnetic field produced by a current loop of finite radius through a coaxial circular aperture in a perfectly conducting plate is evaluated through a rapidly convergent formulation in an exact form.
Giampiero Lovat +3 more
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A complete and partial integrability technique of the Lorenz system
Results in Physics, 2018 In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage
Lazhar Bougoffa +2 more
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Solutions to Abel’s Integral Equations in Distributions [PDF]
Axioms, 2018 The goal of this paper is to study fractional calculus of distributions, the generalized Abel’s integral equations, as well as fractional differential equations in the distributional space D ′ ( R + ) based on inverse convolutional operators and Babenko’s approach.
Chenkuan Li +2 more
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A Special Abel's Integral Equation
Missouri Journal of Mathematical Sciences, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Risteski, Ice B. +2 more
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IET Microwaves, Antennas & Propagation, 2021 The radiation of a double‐layer spherical dielectric lens equipped with a conformal spherical‐disk PEC reflector and excited by elementary sources located on the antenna axis of rotation is considered. The sources are either a radial electric dipole or a
Maria E. Tikhenko +3 more
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