An efficient numerical method for fractional model of allelopathic stimulatory phytoplankton species with Mittag-Leffler law

Behzad Ghanbari; Devendra Kumar; Jagdev Singh

doi:10.3934/dcdss.2020428

Article Contents

2021, Volume 14, Issue 10: 3577-3587. Doi: 10.3934/dcdss.2020428

This issue Previous Article Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters Next Article Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator

An efficient numerical method for fractional model of allelopathic stimulatory phytoplankton species with Mittag-Leffler law

1.
Department of Engineering Science, Kermanshah University of Technology, Kermanshah, Iran, Department of Mathematics, Faculty of Engineering and Natural Sciences, Bahçeşehir University, 34349 Istanbul, Turkey
2.
Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
3.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India

^* Corresponding author: jagdevsinghrathore@gmail.com
^* Corresponding author: jagdevsinghrathore@gmail.com

Received: November 30, 2019

Revised: February 29, 2020

Early access: September 2020

Published: October 2021

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Abstract

The principal aim of the present article is to study a mathematical pattern of interacting phytoplankton species. The considered model involves a fractional derivative which enjoys a nonlocal and nonsingular kernel. We first show that the problem has a solution, then the proof of the uniqueness is included by means of the fixed point theory. The numerical solution of the mathematical model is also obtained by employing an efficient numerical scheme. From numerical simulations, one can see that this is a very efficient method and provides precise and outstanding results.

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Mathematics Subject Classification: Primary:26A33, 34A08;Secondary:37N25.

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Figure 1. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.001 $.

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Figure 2. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.002 $.

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Figure 3. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.003 $.

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Figure 4. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.005 $.

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Figure 5. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.05 $.

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Figure 6. Influence of $ \rho $ on response behavior of solutions when $ \gamma = 0.01 $.

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