# Analyze the Eigenvalues of a Neutral Delay Differential Equation by Employing the Generalized Lambert W Function

## Authors

• K. Sasikala Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India https://orcid.org/0000-0002-7782-5989
• D. Piriadarshani Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India https://orcid.org/0000-0002-4042-0232
• Vediyappan Govindan Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India https://orcid.org/0000-0003-4750-1964
• M. Ijaz Khan Department of Mechanical Engineering, Lebanese American University, Kraytem, Beirut 1102-2801, Lebanon https://orcid.org/0000-0002-9041-3292
• Manish Gupta Division of Research and Technology, Lovely Professional University, Phagwara 1444, India
• Artur Zayniddinovich Koryogdiev Chief Accountant, Jizzakh State Pedagogical University, Jizzakh 130100, Uzbekistan
• Almetwally M. Mostafa Department of Information Systems, College of Computers and Information Science, King Saud University, Riyadh 11421, Saudi Arabia https://orcid.org/0000-0002-0976-239X
• Nouf F. AlQahtani Department, College of Education, King Saud University, Riyadh 11421, Saudi Arabia

## Keywords:

neutral delay differential equation, Lambert W function, characteristic root

## Abstract

In this paper the authors discuss a class of differential equations known as neutral delay differential equations (NDDEs) in which the delay occurs in the derivative with the highest order. They are encountered in various fields of applied sciences and are essential for mathematically representing real-world phenomena. It was challenging to discover approximate analytical solutions for certain methods. In this study, the researchers utilized the generalized Lambert W function to derive the characteristic roots for a first-order neutral delay differential equation featuring random delays. Numerical examples were then utilized to validate the obtained results.

2024-04-16

## How to Cite

1.
Sasikala K, Piriadarshani D, Govindan V, Khan MI, Gupta M, Koryogdiev AZ, Mostafa AM, AlQahtani NF. Analyze the Eigenvalues of a Neutral Delay Differential Equation by Employing the Generalized Lambert W Function. Contemp. Math. [Internet]. 2024 Apr. 16 [cited 2024 May 28];5(2):1662-71. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3909

Research Article