For the constant frequency case, we introduce a special type of Ermakov-Pinney equations with nonlinear dissipation based on the corresponding Chiellini integrable Abel equation. General solutions of these equations are obtained following the Abel equation route. Based on particular solutions, we also provide general solutions containing a factor with the phase of the Milne type. In addition, t...

A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier proposed methods was restricted to the numerical inversion of a part of the generalized Abel integral equation. The method is quite accurate and stable as illustrated by applying it to intensity data...

Convergence of power series solutions for a class of non-linear Abel type equations, including an equation that arises in nonlinear cooling of semi-infinite rods, is very slow inside their small radius of convergence. Beyond that the corresponding power series are wildly divergent. Implementation of nonlinear sequence transformation allow effortless evaluation of these power series on very larg...

This has been seen that in some application for finding the analytical solution of mathematical problem is too complicated , so in recent years researcher has devoted lots of afforts to find the numerical solution of the equation. In this paper an application of the Gegenbauer wavelet method is applied to solve system of generalized Abel's integral equation. This wavelet reduces the system...

An Abel di erential equation y p x y q x y is said to have a center at a pair of complex numbers a b if y a y b for any its solution y x with the initial value y a small enough Let p q be polynomials and let P R p Q R q P and Q satisfy Polynomial Composition condition if there exist polynomials P Q and W such that P x P W x Q x Q W x and W a W b The main result of this paper is that for a xed p...