On initial value problems of fractal delay equations

•We have formulated fractal functional differential equations.•Fractal delay equations are classified and solved.•Fractal linear delay differential equations are solved. In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phenomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of steps and using Laplace transform. The graphs of solutions are given to show the details.