Application of Caputo-Fabrizio operator to suppress the Aedes Aegypti mosquitoes via Wolbachia: An LMI approach

The aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo-Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular kernel which was introduced by Caputo and Fabrizio. Secondly, we have created a mathematical model to increase Cytoplasmic Incompatibility (CI) in Aedes Aegypti mosquitoes by releasing Wolbachia infected mosquitoes. By this, we can suppress the population density of A.Aegypti mosquitoes and can control most common mosquito-borne diseases such as Dengue, Zika fever, Chikungunya, Yellow fever and so on. Our main aim in this paper is to examine the behaviours of Caputo-Fabrizio operator over the logistic growth equation of a population system then, prove the existence and uniqueness of the solution for the considered mathematical model using CF operator. Also, we check the alpha-exponential stability results for the system via linear matrix inequality technique. Finally a numerical example is provided to check the behaviour of the CF operator on the population system by incorporating the real world data available in the known literature. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

The aim of this paper is to establish stability results for a mathematical model using the approach of Linear Matrix Inequality (LMI) and the Caputo-Fabrizio operator (CF operator). The paper extends existing results of the Caputo fractional derivative and creates a mathematical model to control mosquito-borne diseases by increasing cytoplasmic incompatibility in Aedes Aegypti mosquitoes. The paper examines the behavior of the CF operator on the population system and proves the existence and uniqueness of the solution for the mathematical model using CF operator.