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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Centers for Trigonometric Abel Equations [PDF]
Qualitative Theory of Dynamical Systems, 2011 El títol de la versió pre-print de l'article és: Strongly persistent centers for trigonometric Abel equations In this paper we introduce the notion of strongly persistent centers, together with the condition of the annulation of some generalized moments, for Abel differential equations with trigonometric coefficients as a natural candidate to ...
Cimà, Anna +2 more
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A Chiellini type integrability condition for the generalized first kind Abel differential equation [PDF]
, 2013 The Chiellini integrability condition of the first order first kind Abel equation $dy/dx=f(x)y^2+g(x)y^3$ is extended to the case of the general Abel equation of the form $dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}$, where $\alpha \in \Re$, and ...
Harko, Tiberiu +2 more
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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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Le critère d’Abel pour la résolubilité par radicaux d’une équation irréductible de degré premier
Comptes Rendus. Mathématique, 2021 In his last letter to Crelle, Abel states a criterion for the solvability by radicals of an irreducible equation of prime degree. Sylow finds Abel’s statement ambiguous, and writes that it should be modified.
Deligne, Pierre
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Evolution of spherical cavitation bubbles: parametric and closed-form solutions [PDF]
, 2016 We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the ...
Haret C. Rosu +5 more
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On Smoothness of the Solution to the Abel Equation in Terms of the Jacobi Series Coefficients
Axioms, 2020 In this paper, we continue our study of the Abel equation with the right-hand side belonging to the Lebesgue weighted space. We have improved the previously known result— the existence and uniqueness theorem formulated in terms of the Jacoby series ...
Maksim V. Kukushkin
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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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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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Nonlinear Abel type integral equation in modelling creep crack propagation [PDF]
, 2011 Copyright @ 2011 Birkhäuser BostonA nonlinear Abel-type equation is obtained in this paper to model creep crack time-dependent propagation in the infinite viscoelastic plane. A finite time when the integral equation solution becomes unbounded is obtained
G.N. Savin +9 more
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