Representation of solutions of difference equations with continuous time

Abstract

This paper describes a representation of solutions of the system of nonautonomous functional equations x(t) = A(t)x(t - 1) + B(t)x(p(t)), in form of series, using the Cauchy matrix of the linear system y(t) = A(t)y(t - 1). A representation of analitical solutions of the equation x(t) = ax(t - 1) + bx(pt) with constant coefficients is also investigated.