Results 11 to 20 of about 54,600 (268)
Integrable Abel equations and Vein's Abel equation [PDF]
Mathematical Methods in the Applied Sciences, 2016 We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic ...
Mancas, Stefan C., Rosu, Haret C
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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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Planar nonautonomous polynomial equations V. The Abel equation [PDF]
Opuscula Mathematica, 2013 We give a full description of the dynamics of the Abel equation \(z'=z^3+f(t)\) for some special complex valued \(f\). We also prove the existence of at least three periodic solutions for equations of the form \(z'=z^n+f(t)\) for odd \(n \geq 5\).
Paweł Wilczyński
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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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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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Abel fractional differential equations using Variation of parameters method
Ratio Mathematica, 2022 The Variation of Parameters Method (VPM) is utilized throughout the research to identify a numerical model for a nonlinear fractional Abel differential equation (FADE).
Nithya Devi, P. Prakash
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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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Rational limit cycles of Abel differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo +2 more
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