Thai Journal of Mathematics Volume 10 (2012) Number 1 : 43–57 www.math.science.cmu.ac.th/thaijournal Online ISSN 1686-0209 A New Application of Homotopy Analysis Method Mojtaba Ghanbari †, 1 and Tofigh Allahviranloo ‡ † Department of Mathematics, Aliabad Katoul Branch Islamic Azad University, Aliabad Katoul, Iran e-mail : Mojtaba.Ghanbari@gmail.com ‡ Department of Mathematics, Sciences and Research Branch Islamic Azad University, Tehran, Iran e-mail : tofigh@allahviranloo.com Abstract : In this paper, we focus on linear fuzzy Fredholm integral equations of the second kind and propose a new method for solving it, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter . The results illustrate the validity and the great potential of the HAM in solving fuzzy integral equations. Keywords : Fuzzy functions; Fuzzy numbers; Fuzzy integral equations; Homotopy analysis method. 2010 Mathematics Subject Classification : 45A05; 45B05; 45F05; 74S30. 1 Introduction The topics of fuzzy integral equations which growing interest for some time, in particular in relation to fuzzy control, have been rapidly developed in recent years. We know that solving fuzzy integral equations requires appropriate and applicable definitions of fuzzy function and fuzzy integral of a fuzzy function. The fuzzy mapping function was introduced by Chang and Zadeh [1]. Later, Dubois and Prade [2] presented an elementary fuzzy calculus based on the extension principle 1 Corresponding author email: Mojtaba.Ghanbari@gmail.com (M. Ghanbari) Copyright c  2012 by the Mathematical Association of Thailand. All rights reserved.