Systems of equations in differentials with generalised derivatives of continuous functions

Authors

  • Anastasia I. Zhuk Brest State Technical University, 267 Maskowskaja Street, Brest 224023, Belarus
  • Helena N. Zashchuk Brest State Technical University, 267 Maskowskaja Street, Brest 224023, Belarus

Keywords:

algebra of new generalised functions, differential equations with generalised coefficients, functions of finite variation

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 generalized 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 generalized coefficients in the space L(T).

Author Biographies

  • Anastasia I. Zhuk, Brest State Technical University, 267 Maskowskaja Street, Brest 224023, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of higher mathematics, faculty of electronic informational systems

  • Helena N. Zashchuk, Brest State Technical University, 267 Maskowskaja Street, Brest 224023, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of higher mathematics, faculty of electronic informational systems

References

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Published

2024-12-04

Issue

No. 3 (2024): Journal of the Belarusian State University. Mathematics and Informatics

Section

Differential Equations and Optimal Control

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How to Cite

[1]
Zhuk, A.I. and Zashchuk, H.N. 2024. Systems of equations in differentials with generalised derivatives of continuous functions. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2024), 22–30.