This paper focuses on obtaining the exact solution of the functional differential equation:  subject to the initial condition  The standard series approach is applied to obtain the solution in a power series form. The convergence issue is addressed. In addition, the exact solution is established in terms of elementary functions such as hyperbolic and trigonometric functions. The exact solutions of some special cases, at particular choices of a and b, are determined. The obtained results may be introduced for the first time regarding the solution of the current problem.

functional differential equation, exact solution, series solution.

Received: November 5, 2021; Accepted: December 2, 2021; Published: December 20, 2021

How to cite this article: Abdelhalim Ebaid and Hind K. Al-Jeaid, On the exact solution  of the functional differential equation  Advances in Differential Equations and Control Processes 26 (2022), 39-49. DOI: 10.17654/0974324322003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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