Mathematics and Statistics Vol. 8(5), pp. 551 - 558
DOI: 10.13189/ms.2020.080508
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Homotopy Perturbation Method for Solving Linear Fuzzy Delay Differential Equations Using Double Parametric Approach

Ali F Jameel ^1,*, Sardar G Amen ², Azizan Saaban ¹, Noraziah H Man ¹, Fathilah M Alipiah ^1
1 School of Quantitative Sciences, College of Art and Sciences, Universiti Utara Malaysia (UUM), Malaysia
² Department of Financial and Banking, College of Business Administration and Financial Science, Al-Kitab University, Iraq

ABSTRACT

Delay differential equations (known as DDEs) are a broad use of many scientific researches and engineering applications. They come because the pace of the shift in their mathematical models relies all the basis not just on their present condition, but also on a certain past cases. In this work, we propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using the Homotopy Perturbation Method with double parametric form fuzzy numbers. The detailed algorithm of the approach to fuzzification and defuzzificationis analysis is provided. In the initial conditions of the proposed problem there are uncertainties with regard to the triangular fuzzy number. A double parametric form of fuzzy numbers is defined and applied for the first time in this topic for the present analysis. This method's simplicity and ability to overcome delay differential equations without complicating Adomian polynomials or incorrect nonlinear assumptions. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show the features of this proposed method, a numerical example is illustrated, involving first order fuzzy delay differential equation. These findings indicate that the suggested approach is very successful and simple to implement.

KEYWORDS
Fuzzy Delay Differential Equations (FDDE), Homotopy Perturbation Method (HPM), Approximate Methods, Single Parametric form Fuzzy Numbers, Double Parametric form Fuzzy Numbers

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ali F Jameel , Sardar G Amen , Azizan Saaban , Noraziah H Man , Fathilah M Alipiah , "Homotopy Perturbation Method for Solving Linear Fuzzy Delay Differential Equations Using Double Parametric Approach," Mathematics and Statistics, Vol. 8, No. 5, pp. 551 - 558, 2020. DOI: 10.13189/ms.2020.080508.

(b). APA Format:
Ali F Jameel , Sardar G Amen , Azizan Saaban , Noraziah H Man , Fathilah M Alipiah (2020). Homotopy Perturbation Method for Solving Linear Fuzzy Delay Differential Equations Using Double Parametric Approach. Mathematics and Statistics, 8(5), 551 - 558. DOI: 10.13189/ms.2020.080508.