Representation of solutions of a second order delay differential equation

Abstract

In this article, we study an inhomogeneous second order delay differential equation on the fractal set $\mathbb{R}^{\alpha n}$ $(0<\alpha\leq 1)$, based on the theory of local calculus. We introduce delay cosine and sine type matrix functions and give their properties on the fractal set. We give the representation of solutions to second order differential equations with pure delay and two delays.

Keywords

• second order delay differential equations
• delayed matrix functions
• fractal set