Homotopy analysis method approximate solution for fuzzy pantograph equation. (14th December 2021)

• Record Type: Journal Article
• Authors: Shather, A.H.; Jameel, A.F.; Anakira, N.R.; Alomari, A.K.; Saaban, Azizan
• Is Part Of: International journal of computing science and mathematics. Volume 14:Number 3(2021)
• Page Start: 286
• Page End: 300
• Publication Date: 2021-12-14
• Subjects: fuzzy set theory -- fuzzy differential equations -- fuzzy pantograph equation -- FPE -- homotopy analysis method -- HAM; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.