In this paper, the existence of fuzzy solutions for first and second order nonlocal impulsive neutral functional differential equations are studied using Banach fixed point theorem. We used the techniques of fuzzy set theory, functional analysis, and Hausdorff metric. Example is provide to illustrate the theory.Muralisankar [1] explicated the existence and uniqueness of fuzzy solution for the nonlinear fuzzy integrodifferential equations. Recently, Ramesh and Vengataasalam [5] examined the solutions of fuzzy impulsive delay integrodifferential equations with nonlocal condition. Vengataasalam and Ramesh [6] studied the fuzzy solutions for impulsive semilinear differential equations. For more on fuzzy differential equations, refer to [7,8]. Neutral differential equations are used in many areas of applied mathematics and due to its vast applications these equations are given much attention in recent years. These equations have major impact in the field of biological and engineering processes; for details, see [9,10]. The theory of ordinary Neutral Functional Differential Equations (NFDE) was initially developed by Bellman and Cooke [11]. Then it was developed by Cruz and Hale [12], Hale [13,14], Hale and Meyer [15], and Henry [16]. They developed the basic theory of existence and uniqueness, and also the properties of the solution operator and stability. Many authors contributed to the field of NFDE [17,18,19,20]. Benchohra [18] studied neutral functional differential and integrodifferential inclusions for nonlocal Cauchy problems in Banach spaces. Balachandran and Sakthivel [19] examined the existence of solutions of neutral functional integrodifferential equation in Banach spaces. Many works dealing the existence results of mild solutions for first and second order abstract partial neutral differential systems which are similar to (3.1) − (3.3) and (3.4) − (3.7), were published. Balachandran and Dauer [20] investigated the existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces. Balachandran and Anthoni [21] analyzed the existence of solutions of second order neutral functional differential equations. See, for example, [18,22,23] for the first order case and [24,22,25] for the second order. The study of impulsive functional differential equation is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution. The perturbations are performed discretely and their duration is negligible in comparison with the total duration of the processes and phenomena. We refer to the monographs of Bainov and Simeonov [26], Benchohra et al. [27], Lakshmikantham et al. [28], and Samoilenko and Perestyuk [29] where numerous properties of their solutions are studied, and the detailed bibliographies are given. This paper is concerned with the existence of fuzzy solutions for more general initial value problems of first and second order impulsive neutral functional differential equations. Moreover, to the author's knowledge, there are few pa...
