Mathematics and Statistics 11(6): 923-935, 2023 DOI: 10.13189/ms.2023.110607 http://www.hrpub.org Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations V. Padmapriya 1,2 , M. Kaliyappan 1,* 1 Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India 2 New Prince Shri Bhavani Arts and Science College, Chennai, India * Corresponding Author: kaliyappan.m@vit.ac.in, v.padmapriya2015@vit.ac.in Received June 22, 2023; Revised September 22, 2023; Accepted October 12, 2023 Cite This Paper in the following Citation Styles (a): [1] V. Padmapriya, M. Kaliyappan, ”Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations,” Mathematics and Statistics, Vol.11, No.6, pp. 923-935, 2023. DOI: 10.13189/ms.2023.110607 (b): V. Padmapriya, M. Kaliyappan (2023). Adomian Decomposition Method for Solving Fuzzy Hilfer Fractional Differential Equations. Mathematics and Statistics, 11(6), 923-935. DOI: 10.13189/ms.2023.110607 Copyright ©2023 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract The field of fractional calculus is mainly con- cerned with the differentiation as well as integration of arbitrary orders. This concept is obviously present in various domains of science and engineering. Most people are familiar with the Caputo and Riemann-Liouville fractional definitions. Recently, Hilfer has related the Caputo and Riemann-Liouville derivatives by a general formula; this connection is referred to as the Hilfer or generalized Riemann-Liouville derivative. The Hilfer fractional derivative serves as an intermediary between the Riemann-Liouville and Caputo fractional deriva- tives, providing a means of interpolation. Parameters in the Hilfer derivative provide more degrees of freedom. Adomian decomposition method (ADM) is widely regarded as a highly effective mathematical technique for solving both linear and nonlinear differential equations. ADM provides an analytical solution in the form of a series solution. Motivated by the growing number of real-life applications for fractional calculus, the objective of this work is to explore the solutions of Hilfer fractional differential equations in a fuzzy sense using the ADM. The efficiency and accuracy of the proposed method are demonstrated by the solution of numerical exam- ples. Graphical representations are provided to visualize the solutions’ behavior. This shows that as the number of terms in the series goes up, the numerical results get closer and closer to the exact solutions. Keywords Fuzzy Fractional Differential Equations, Riemann-Liouville Fractional Derivative, Caputo Fractional Derivative, Hilfer Fractional Derivative, Adomian Decompo- sition Method 1 Introduction The topic of the fractional differential equation has received a lot of attention from authors interested in fractional calculus because of its essential application in the modeling of nu- merous occurrences in diverse fields of science, engineering, mathematics, bioengineering, and so on. Recent years have seen incredible progress in the study of ordinary, partial differential, and integral equations of fractional order. For more information, see Kilbas et al. [1], Lakshmikantham et al. [2], Miller and Rose [3], and Podlubny [4]. Fractional derivatives and integrals can be defined in a number of ways in the existing literature. Among these, the Riemann-Liouville and Caputo fractional definitions are the most prominent. Recently, the Riemann-Liouville fractional derivative has been generalized by Hilfer in [5]. Several authors refer to this type of derivative as the Hilfer derivative. The parameters in Hilfer fractional derivative add an additional degree of freedom to the initial conditions and generate a wider range of steady states. We refer the reader to a series of works [6]-[14] in which references to some recent results and applications of the Hilfer fractional derivative are provided. However, researchers have proposed fuzzy fractional differential equations (FFDEs) to deal with uncertainty in various dynamical problems that exhibit imprecision, ambiguity, and non-normal dynamical behaviors with long memory or hereditary effects. The approaches of Caputo, Riemann-Liouville, Caputo-Katugampola, Hadamard, and Caputo-Hadamard are widely recognized in the field of fuzzy fractional derivatives and have been extensively studied and researched in the existing literature. More precisely, Agarwal et al. [15] and Allahviranloo et al. [16] investigated theoretical