Fractional modeling of plankton-oxygen dynamics under climate change by the application of a recent numerical algorithm

Abstract

This research work is dedicated to studying the dynamics of a coupled plankton-oxygen model in the framework of three non-linear differential equations. As we know that the ocean dynamics have a firm impact on the global climate change and on the creation of the environment. Also, it is recorded that about 70% of the environmental oxygen is manufactured in the oceans due to the photosynthetic bustling of phytoplankton. All the same, the rate of oxygen manufacture based on the temperature of the water and hence can be dominance by global warming. To study the proposed Oxygen-Phytoplankton-Zooplankton system, we use a very recent fractional numerical algorithm. We discuss the existence of the solution for the given model problem because in the case of fractional-order models, the proof of solution existence always becomes an important task. After that, we perform many novel 2-D and 3-D graphs by using Mathematica and Python software to fulfill the requirements of the numerical simulations. We use a generalised form of the well known Liouville-Caputo fractional derivative. Given numerical algorithm is very recent, short, easy, and reliable to use or to apply to the non-linear dynamical models. The main motive of this research work is to study the Plankton-Oxygen dynamics under the climate change by using the proposed fractional-order model with capturing the memory effects and discuss some novel results for the literature on such ecological topics.