We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve. We show that the solution is non-trivial if and only if corresponding Poncelet problem for two conics associated with the curve has periodic trajectory and if and only if corresponding Pell–Abel equation has a solution.

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of differential equation of integer order connected with inverse forms of Abel-integral equations. The algorithm is used for solution of the linear and non-linear equati...

This article provides sufficient conditions for the existence of periodic solutions with nonconstant sign in a family of polynomial, non-autonomous, first-order differential equations that arise as a generalization of the Abel equation of the second kind.

We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C[0, 1]. The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

in this paper , numerical solotion of abel's integral equationby using the taylor expanssion of the unknown functionvia collection method based on sinc is considered...