Electron. J. Differential Equations, Vol. 2020 (2020), No. 72, pp. 1-20

Representation of solutions of a second order delay differential equation

Kee Qiu, Jinrong Wang

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.

Submitted March 24, 2020. Published July 7, 2020.
Math Subject Classifications: 26A33, 28A80, 34A34.
Key Words: Second order delay differential equations; delayed matrix functions; fractal set.

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Kee Qiu
School of Mathematics and Big Data
Guizhou Education University
Guiyang, Guizhou 550018, China
email: qke456@sina.com
Jinrong Wang
Department of Mathematics
Guizhou University
Guiyang, Guizhou 550025, China
email: jrwang@gzu.edu.cn

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