Title: Homotopy analysis method approximate solution for fuzzy pantograph equation

Authors: A.H. Shather; A.F. Jameel; N.R. Anakira; A.K. Alomari; Azizan Saaban

Addresses: Department of Communication Engineering, Technical College of Engineering (TCE), Sulaimiani Polyechic University, Kurdistan Region, Iraq ' School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Kedah, Sintok, 06010 Malaysia ' Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan ' Department of Mathematics, Faculty of Science, Yarmouk University, Irbid 211-63, Jordan ' School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Kedah, Sintok, 06010 Malaysia

Abstract: This paper investigates the powerful method namely the homotopy analysis method (HAM), to solve the fuzzy pantograph equation (FPE) in approximate analytic form. HAM yields a convergent infinite series solution to the solution of FPE without the need to reduce the FPE to the first order system or compare it with the exact solution, and this is one of the advantages of this method. For a better approximate solution, the HAM uses a convergence control parameter from the convergence region of the infinite series solution. HAM solution of FPE is obtained by reformulate crisp standard approximation via the properties of the fuzzy set theory.

Keywords: fuzzy set theory; fuzzy differential equations; fuzzy pantograph equation; FPE; homotopy analysis method; HAM.

DOI: 10.1504/IJCSM.2021.119904

International Journal of Computing Science and Mathematics, 2021 Vol.14 No.3, pp.286 - 300

Received: 25 Mar 2019
Accepted: 13 May 2019
Published online: 23 Dec 2021 *

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