On initial value problems of fractal delay equations

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 phe-nomena 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 us-ing Laplace transform. The graphs of solutions are given to show the details.(c) 2023 Elsevier Inc. All rights reserved.

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This paper provides a brief summary of fractal calculus, presenting fractal functional differential equations as a mathematical model for phenomena with fractal time and structure. The method of steps and Laplace transform are used to solve fractal retarded, neutral, and renewal delay differential equations with constant coefficients, and the graphs of solutions are provided to illustrate the details.