Volume 11, Issue 4 (April 2024), Pages: 85-92

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 Technical Note

Applying the fuzzy homotopy analysis method to solve fuzzy initial value problems with variable coefficients

 Author(s): 

 Raad I. Khwayyit ^1, *, Mazin H. Suhhiem ²

 Affiliation(s):

 ¹Ministry of Education, Baghdad, Iraq
 ²Department of Mathematics, University of Sumer, Al-Rifa'i District, Iraq

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0009-0005-1416-0480

 Digital Object Identifier (DOI)

 https://doi.org/10.21833/ijaas.2024.04.010

 Abstract

In this study, we applied the fuzzy homotopy analysis method to find an approximate but analytical solution to initial value problems that have fuzzy variable coefficients. These coefficients were represented by triangular fuzzy functions. This approach lets us solve the fuzzy differential equations as an endless series of fuzzy numbers, where each fuzzy component can be determined without much difficulty. Based on the numerical data we analyzed, the series solutions we arrived at are both precise and closely match the exact analytical solutions for fuzzy problems.

 © 2024 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Fuzzy homotopy analysis method, Fuzzy initial value problems, Fuzzy variable coefficients, Triangular fuzzy functions, Approximate analytical solution

 Article history

 Received 24 August 2023, Received in revised form 25 February 2024, Accepted 31 March 2024

 Acknowledgment 

No Acknowledgment.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Khwayyit RI and Suhhiem MH (2024). Applying the fuzzy homotopy analysis method to solve fuzzy initial value problems with variable coefficients. International Journal of Advanced and Applied Sciences, 11(4): 85-92

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