Title: A new approximate solution of the fuzzy delay differential equations

Authors: A.F. Jameel; N.R. Anakira; A.K. Alomari; M. Al-Mahameed; A. Saaban

Addresses: School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, Malaysia ' Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, 2600, Jordan ' Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 211-63, Jordan ' Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, 2600, Jordan ' School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Sintok, 06010 Kedah, Malaysia

Abstract: In this paper, an approximate analytical algorithm namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of first order fuzzy delay differential equations (FDDEs). This method allows for the solution of the FDDEs to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter the convergence region of the infinite series solution. Numerical examples are tested to highlight the important features of the HAM algorithm.

Keywords: fuzzy number; fuzzy differential equation; delay differential equation; DDE; homotopy analysis method; HAM.

DOI: 10.1504/IJMMNO.2019.100476

International Journal of Mathematical Modelling and Numerical Optimisation, 2019 Vol.9 No.3, pp.221 - 240

Received: 24 Jan 2018
Accepted: 21 Apr 2018
Published online: 29 Jun 2019 *

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