INDIAN JOURNAL OF SCIENCE AND TECHNOLOGY RESEARCH ARTICLE OPEN ACCESS Received: 05-02-2023 Accepted: 11-08-2023 Published: 04-12-2023 Citation: Savla SL, Sharmila RG (2023) Solving Fuzzy Fractional Biological Population Model using Shehu Adomian Decomposition Method. Indian Journal of Science and Technology 16(SP3): 44-54. http s://doi.org/ 10.17485/IJST/v16iSP3.icrtam151 * Corresponding author. gethsi.ma@bhc.edu.in Funding: None Competing Interests: None Copyright: © 2023 Savla & Sharmila. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee) ISSN Print: 0974-6846 Electronic: 0974-5645 Solving Fuzzy Fractional Biological Population Model using Shehu Adomian Decomposition Method S Luvis Savla 1 , R Gethsi Sharmila 2* 1 Research Scholar, PG & Research Department of Mathematics, Bishop Heber College, (Affiliated to Bharathidasan University), Tiruchirappalli-17, Tamil Nadu, India 2 Associate Professor, PG & Research Department of Mathematics, Bishop Heber College, (Affiliated to Bharathidasan University), Tiruchirappalli-17, Tamil Nadu, India Abstract Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) are a crucial topic. The main objective of this study is to find the exact solution of the nonlinear Fuzzy Fractional Biological Population Model (FFBPM). In the Caputo concept, fractional derivatives are regarded. Methods: For nonlinear problems, the Shehu transform is difficult to exist. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian Decomposition Method (SHADM) and has been proposed to solve the FFBPM. Findings: The main favor of this method is rapidly converging to the exact solution for nonlinear FFDEs. The theoretical proof of convergence for the SHADM and the uniqueness of the solution is given. Novelty: Adomian polynomials are used for nonlinear terms. Figures and numerical examples demonstrate the expertise of the suggested approach. This method is applied for both linear and nonlinear ordinary and partial FFDEs. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes. Keywords: Caputo fractional derivative; Shehu transform; triangular fuzzy number; Fuzzy Fractional Biological Population Model; Shehu Adomian decomposition method 1 Introduction Fractional calculus is expanded upon in ordinary calculus. is involves computing a function’s derivative in any order. e memory and heredity characteristics of numerous substances and processes in porous media, electrical circuits, control, biology, electromagnetic processes, biomechanics, and electro chemistry have been documented using fractional differential operators. Over the past few decades, fractional calculus and its applications have gained popularity, mostly because it has proven to be a helpful tool for modelling a number of complex processes in a wide range of seemingly unrelated fields of science and engineering. Measurement uncertainty is represented by a fuzzy number. Since its invention by Lotfi Zadeh in 1965, fuzzy sets have found utility in a variety of contexts. https://www.indjst.org/ 44