J. Math. Computer Sci., 23 (2021), 67–74 Online: ISSN 2008-949X Journal Homepage: www.isr-publications.com/jmcs Numerical solutions of fuzzy integro-differential equations of the second kind Mohammed S. Bani Issa a , Ahmed A. Hamoud b,* , Kirtiwant P. Ghadle c a Department of Mathematics, P. E. T. Research Foundation, University of Mysore, Mandya 570401, India. b Department of Mathematics, Taiz University, Taiz, Yemen. c Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India. Abstract In this paper, the Adomian decomposition method, modified Adomian decomposition method, variational iteration method, and homotopy perturbation method are used to solve the fuzzy integro-differential equations. We described the methods and compared the results with their exact solutions to demonstrate the methods’ validity and applicability. Examples are provided to illustrate the results. Keywords: Fuzzy integro-differential equations, Adomian decomposition method, modified Adomian decomposition method, variational iteration method, homotopy perturbation method. 2020 MSC: 34A07, 49M27, 65K10, 65H20. c 2021 All rights reserved. 1. Introduction The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Later, the area of interest in fuzzy integral equations has been expanded into the fuzzy integro-differential equations (FIDEs). The study of FIDEs forms a suitable setting for mathematical modeling of real-world problems in which uncertainties or vagueness pervade. The topics of FIDEs which is a growing interest for some time, in particular in relation to fuzzy control, have been rapidly developed in recent years [6]. The existence and uniqueness of solutions of FIDEs were investigated by Park and Jeong in [16], Hajighasemi et al. in [7], and Zeinali et al. in [17]. Mikaeilvand et al. in [15] presented the numerical examples of FIDEs using the differential transform method. In [1, 2], Allahviranloo et al. proposed a new technique to solve the FIDEs using definition of generalized differentiability. Hamoud and Ghadle in [11] presented the homotopy analysis method for the first order fuzzy Volterra-Fredholm integro-differential equations. * Corresponding author Email address: drahmedselwi985@gmail.com (Ahmed A. Hamoud) doi: 10.22436/jmcs.023.01.07 Received: 2020-06-05 Revised: 2020-07-09 Accepted: 2020-08-25