Fractional Modeling of Fish Growth with Visual Analysis

Abstract

In this paper, we analyze the fractional version of mathematical model for the allometric equation in sense of Caputo, Atangana–Baleanu (ABC) and Caputo–Fabrizio (CFC) fractional derivatives. We derive approximation solutions by means of Laplace Adomian decomposition method (LADM). This techniques is applied to obtain analytic and approximation solutions for nonlinear fractional order differential equations. Applying Banach and Krasnoselskii fixed point theorem, we prove theorems of existence and uniqueness of solution for growth model in frame of CFC derivative. Also, we present comparatively visual results of the solutions by graphs with different orders of ? and ?. Simulation analysis is performed for sheding more light on the physical features of the growth models. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.