A Fractional Model of Abalone Growth using Adomian Decomposition Method

TL;DR

This paper introduces a fractional order growth model for abalone using the Adomian decomposition method, demonstrating improved accuracy over classical models by incorporating fractional calculus.

Contribution

It develops a fractional growth model based on the McKendrick equation and shows its enhanced predictive accuracy using the Adomian decomposition method.

Findings

Higher fractional orders lead to larger series values.

A fractional order of 0.5 best fits real data.

Fractional model outperforms classical integer order models.

Abstract

This study is a modification of the McKendrick equation into a growth model with fractional order to predict the abalone length growth. We have shown that the model is a special case of Taylor's series after it was analysed using Adomian decomposition method and Caputo fractional derivative. By simulating the series with some fractional orders, the results indicate that the greater the fractional order of the model, the series values generated are greater as well. Moreover, the series that is close to the real data is the one with a fractional order of $0.5$. Therefore, the growth model with a fractional order provides more accuracy than a classical integer order.