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This paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability
Published Online First 30/4/2021
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Farlow SJ. An introduction to differential equations and their applications. Mineola, New York: Dover Publications, Inc.; 1994.
Baraniuk R. Signals and systems. Connexions Rice University, Houston, Texas; 2008. Online: http://cnx.org /content/col10064/1.11/.
Yi S, Yu S, Kim JH. Analysis of neural networks with time-delays using the Lambert W function. InProceedings of the 2011 American Control Conference 2011 Jun 29 (pp. 3221-3226). IEEE. 2011; 3221- 3226. doi: 10.1109/ACC.2011.5991085.
Sujitha SS, Piriadarshani D. A Lambert W function a approach for solution of second order delay differential equation as a special case of the one- mass system controlled over the network. Int. J. Mech. Eng. Technol. 2017; 8(10): 502–511.
Jadlovska I. Application of Lambert W function in oscillation theory. Acta electrotech. inform. 2014; 14(1): 9-17.
Chen ST, Hsu SP, Huang HN, Yang BY. Time response of a scalar dynamical system with multiple delays via Lambert W functions. arXiv preprint arXiv:1609.02034. 2016 Sep 7.
Abdullah HK, Haydar AK, Obead KR. Solving of third order retarded dynamical systems via Lambert W function and stability analysis. World Wide Journal of Multidisciplinary Research and Development. 2018; 4(3): 105-112.
Abdullah HK, Haydar AK, Obead KR. Solving retarded dynamical system of nth- order and stability analysis via Lambert W function. Int. J. Pure Appl. Math. 2018; 18(20): 2567-2584.
Abdullah HK, Haydar AK, Obead KR. Characteristic roots of a second order retarded functional differential equation via spectral-tau method. J. Nonlinear Sci. Appl. 2020; 13(3): 147-153. doi: 10.22436/jnsa.013.03.03.
Pospíšil M, Jaroš F. On the representation of solutions of delayed differential equations via Laplace transform. Electron. J. Qual. Theory Differ. Equ. 2016; 117: 1-13.
Perko L. Differential equations and dynamical systems. 3rd ed. New York: Springer- Verlag; 2001.
Samer E, Mudar I, Jawad E. Stability and density of periodic points of space 0 < p < 1. Int. Journal of Math. Analysis. 2013; 7(34): 1673-1684.