Differential equations and Optimal control

Systems of equations in differentials with generalised derivatives of continuous functions

A. I. Zhuk, H. N. Zashchuk

Brest State Technical University, 267 Maskowskaja Street, Brest 224023, Belarus

Abstract: Herein, we investigate systems of nonautonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of nonautonomous differential equations with generalised coefficients as a system of equations in differentials in the algebra of new generalised functions. The solution of such a system is a new generalised function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalised functions. In this paper, for the first time in the literature, we describe associated solutions of the system of nonautonomous differential equations with continuous generalised coefficients in the space $L(T)$.

Keywords: algebra of new generalised functions; differential equations with generalised coefficients; functions of finite variation

UDC: 519.9

Received: 12.03.2024
Revised: 20.10.2024
Accepted: 20.10.2024

Language: English