Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Cz?stochowska, Scientific Research the Institute Computer Science, Czestochowa University Technology

We consider the half-linear second order differential equation which is viewed as a perturbation of the so-called Riemann-Weber half-linear differential equation. We present a comparison theorem with respect to the power of the half-linearity in the equation under consideration. Our research is motivated by the recent results published by J. Sugie, N.Yamaoka, Acta Math. Hungar. 111 (2006), 165–...

We study the generalized half-linear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new conjugacy criterion for the generalized half-linear equation.

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...

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of n linear differential polynomial parametric equations in n− 1 differential parameters. We give necessary conditions to ensure properness of the system of differential polynom...