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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 ...
Chenkuan Li +2 more
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Integrable Abel equations and Vein's Abel equation [PDF]
Mathematical Methods in the Applied Sciences, 2015 12 pages, 4 figures, 17 references, online at Math. Meth. Appl. Sci.
Mancas, S. C., Rosu, H. C.
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A spectral Chelyshkov wavelet method to solve systems of nonlinear weakly singular Volterra integral equations [PDF]
Journal of Mahani Mathematical Research, 2020 Based on Chelyshkov wavelet, an operational matrix of integration is extracted, and then is applied for solving linear and nonlinear Abel and systems of Abel integral equations.
Mahmoud Mohseni Moghadam +2 more
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Results in Applied Mathematics, 2022 This article discusses the development of a new algorithm, which is based on optimal quadrature formulas for obtaining solutions to the generalized Abel integral equations.
Kholmat M. Shadimetov +1 more
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Generalized symmetries, first integrals, and exact solutions of chains of differential equations [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied.
C. Muriel, M. C. Nucci
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Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation
Journal of Mathematics, 2022 This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix.
Ioannis Dassios +2 more
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Karpatsʹkì Matematičnì Publìkacìï, 2022 In the paper, we investigate an asymptotic behavior of the sharp upper bounds in the integral metric of deviations of the Abel-Poisson integrals from functions from the class $L^{\psi}_{\beta, 1}$.
T.V. Zhyhallo, Yu.I. Kharkevych
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The solution of the full matrix analogue of the generalized Abel equation with constant coefficients
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011 The system of generalized integral Abel equations in the matrix form with constant coefficients on the segment. Was considered at the terms of the integral Riemann–Liouville operators of matrix order.
R. R. Ismagiliva
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The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation
JTAM (Jurnal Teori dan Aplikasi Matematika), 2023 Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two ...
Muhammad Taufik Abdillah +2 more
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Approximate solution of Abel integral equation in Daubechies wavelet basis
Cubo, 2021 This paper presents a new computational method for solving Abel integral equation (both first kind and second kind). The numerical scheme is based on approximations in Daubechies wavelet basis. The properties of Daubechies scale functions are employed to
Jyotirmoy Mouley +2 more
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