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An Abstract Second Kind Fredholm Integral Equation with Degenerated Kernel

Wysocki, Hubert;  Zellma, Marek — 2005

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 44A40, 45B05 The paper presents an abstract linear second kind Fredholm integral equation with degenerated kernel defined by means of the Bittner operational calculus. Fredholm alternative for mutually conjugated integral equations is also shown here. Some examples of solutions of the considered integral equation in various operational calculus models are also given.

Modulating element method in the identification of a generalized dynamical system

Hubert Wysocki;  Marek Zellma — 1995

Applicationes Mathematicae

In this paper the identification of generalized linear dynamical differential systems by the method of modulating elements is presented. The dynamical system is described in the Bittner operational calculus by an abstract linear differential equation with constant coefficients. The presented general method can be used in the identification of stationary continuous dynamical systems with compensating parameters and for certain nonstationary compensating or distributed parameter systems.

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