On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces

Herein, we investigate systems of non-autonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of non-autonomous 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 non-autonomous differential equations with generalised coefficients in the Lebesgue spaces $L_{P}(T)$.