*Corresponding author Email: mhm.smadi@yahoo.com (Mohammed AL-Smadi) An Iterative Algorithm for Solving Fuzzy Volterra and Fredholm Integro- differential Equations Asad Freihat 1 , Abdel Karim Baareh 1 , Mohammed Al-Smadi 1,* , Qasem Al-Haj Abdullah 2 , and Radwan Abu-Gdairi 2 1 Applied Science Department, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan 2 Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan Abstract This paper investigates the approximate solutions of fuzzy Fredholm and Volterra intergo-differential equations associated to given constraint initial conditions using homotopy analysis method (HAM). The solution was calculated in form of a rapidly convergent series with easily computable components using symbolic computation software. In this method, one has great freedom to select an auxiliary parameter in order to ensure the convergence of the approximate solutions and to increase both the rate and region of convergence. The proposed technique is applied to several examples to illustrate the accuracy, efficiency and applicability of the method. The results reveal that the method is very effective, straightforward and simple. Keywords: Homotopy analysis method; Fuzzy intergo-differential equation; Computer stimulations; Hukuhara differentiability 1 INTRODUCTION The concepts of fuzzy integro-differential equations (FIDEs) have motivated a large amount of research work in recent years. Nonlinear phenomena that appear in many applications in mathematics, physical, and engineering can be modeled by FIDEs. Many experts in such areas extensively use FIDEs in order to make some problems under study more understandable. Usually, data about these problems involved is pervaded with uncertainty, which can arise in the experiment part, data collection, measurement process as well as when determining the initial values. However, classical mathematics cannot cope with this situation. Therefore, it is necessary to have some mathematical apparatus in order to understand this uncertainty [1]. Furthermore, fuzzy calculus theory is a powerful tool for modeling uncertainty and processing vague of subjective information in mathematical models. Their main directions of development have been diverse and its applications to the very varied real problems, including the golden mean, particle systems, quantum optics and chaotic system [2-8]. The HAM was used to investigate several scientific applications side by side with their theory. The reader is asked to refer to [9-14] in order to know more details about fuzzy mathematics. In this paper, we extend the application of the HAM to provide symbolic approximate solution for fuzzy IDE of the Fredholm type:  ′  = ,  +  ,    , ≤, ≤ (1) and the Volterra type:  ′  = ,  +  ,    , ≤ < ≤ (2) subject to the fuzzy initial condition  =  0 , (3) where : ,  × ℝ  →ℝ  , : ,  × ,  × ℝ  →ℝ  , : ℝ  →ℝ  are continuous fuzzy-valued function,  is an unknown function which must be determined,  0 ∈ℝ  , ℝ  denote the set of fuzzy numbers on ℝ and ,  are real finite constants. Anyhow, the numerical solvability of fuzzy initial value problems (FIVPs) those are a special case of Eqs. (1) to (3) have discussed recently by many authors [14-21]; but, generally, investigation about a fuzzy IDEs is scarce, especially, discussion on a nonlinear case. However, FIDEs are almost impossible to solve as well as do not always have solutions by using analytical or semi-analytical techniques. Therefore, it is necessary to develop new