Results 51 to 60 of about 930 (158)

On centers for Generalized Abel Differential Equation

Journal of Zankoy Sulaimani - Part A, 2013
A new condition is given for generalized Abel differential equation to have a center. We apply the results to some polynomial differential systems in the plane to find necessary and sufficient center conditions.
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A connection between Abel and $_p{\rm F}_q$ hypergeometric differential equations

European Journal of Applied Mathematics, 2005
In a recent paper, a new 3-parameter class of Abel type equations, so-called AIR, all of whose members can be mapped into Riccati equations, is shown. Most of the Abel equations with solution presented in the literature belong to the AIR class. Three canonical forms were shown to generate this class, according to the roots of a cubic.
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Properties of the resolvent of a linear Abel integral equation: implications for a complementary fractional equation

Electronic Journal of Qualitative Theory of Differential Equations, 2016
New and known properties of the resolvent of the kernel of linear Abel integral equations of the form \begin{equation} \tag{A$_\lambda$} x(t) = f(t) - \lambda \int_0^t (t - s)^{q-1}x(s)\,ds, \end{equation} where $\lambda > 0$ and $q \in (0,1)$, are ...
Leigh Becker
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NUMERICAL STUDIES FOR SOLVING ABEL'S DIFFERENTIAL EQUATION

Malaysian Journal of Industrial Technology
This paper uses the Abel's Equation, often used in various fields including physics and engineering, represents a mathematical model that can be complex to solve analytically. This research focuses on solving the Abel's Equation using several numerical methods: Euler's method, Taylor series method, Adomian decomposition method, and Runge-Kutta method ...
null T. F. A. Almajbri., null S. S. M. abu-amr, null A. B. Mohammed   +2 more
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From Abel’s differential equations to Hilbert’s 16th problem

São Paulo Journal of Mathematical Sciences
AbstractThe study of the limit cycles of planar polynomial differential equations is motivated both by its appearance in many mathematical models of the real-world as for the second part of Hilbert’s 16th problem. In this work we briefly summarize some results on this subject and we will also highlight the important role that the Abel’s differential ...
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A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions

Mathematics
A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy ...
Xiaohong Chen, Tiecheng Xia, Liancheng Zhu   +2 more
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Bifurcation analysis, and exact solutions of the two-mode Cahn–Allen equation by a novel variable coefficient auxiliary equation method

Results in Physics
This document elaborates on a newly introduced analytical method known as the “Variable Coefficient Generalized Abel Equation Method,” as proposed by Hashemi in Hashemi (2024), designed specifically for addressing the two-mode Cahn–Allen equation ...
Mir Sajjad Hashemi, Mustafa Bayram, Muhammad Bilal Riaz, Dumitru Baleanu   +3 more
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Dynamic Keynesian Model of Economic Growth with Memory and Lag

Mathematics, 2019
A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model.
Vasily E. Tarasov, Valentina V. Tarasova   +1 more
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Solution of Abel Integral Equation Using Differential Transform Method

JOURNAL OF ADVANCES IN MATHEMATICS, 2018
The application of fractional differential transform method, developed for differential equations of fractional order, are extended to derive exact analytical solutions of fractional order Abel integral equations. The fractional integrations are described in the Riemann-Liouville sense and fractional derivatives are described in the Caputo sense.
Subhabrata Mondal, B. N. Mandal
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Mathematical modeling of hereditary elastically deformable body on the basis of structural models and fractional integrodifferentiation Riemann-Liouville apparatus

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2016
The standard one-dimensional generalized model of a viscoelastic body and some of its special cases-Voigt, Maxwell, Kelvin and Zener models are considered. Based on the V. Volterra hypothesis of hereditary elastically deformable solid body and the method
Eugeniy N Ogorodnikov, Vladimir P Radchenko, Luiza G Ungarova   +2 more
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