Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.The research of Juan J. Nieto has been partially supported by Ministerio de Educacion y Ciencia and FEDER, project MTM2007-61724S

An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control

In this paper, a novel age-structured delayed mathematical model to control Aedes aegypti mosquitoes via Wolbachia-infected mosquitoes is introduced. To eliminate the deadly mosquito-borne diseases such as dengue, chikungunya, yellow fever, and Zika virus, the Wolbachia infection is introduced into the wild mosquito population at every stage. This method is one of the promising biological control strategies. To predict the optimal amount of Wolbachia release, the time varying delay is considered. Firstly, the positiveness of the solution and existence of both Wolbachia present and Wolbachia free equilibrium were discussed. Through linearization, construction of suitable Lyapunov–Krasovskii functional, and linear matrix inequality theory (LMI), the exponential stability is also analyzed. Finally, the simulation results are presented for the real-world data collected from the existing literature to show the effectiveness of the proposed model.This article has been written with the joint partial financial support of SERB-EEQ/2019/000365, the National Science Centre in Poland (Grant DEC-2017/25/B/ST7/02888, RUSA Phase 2.0 (Grant No. F 24–51/2014-U), Policy (TN Multi-Gen), Dept.of Edn. Govt. of India, UGC-SAP (DRS-I) (Grant No. F.510/8/DRS-I/2016(SAP-I)), DST-PURSE 2nd Phase programme vide letter No. SR/PURSE Phase 2/38 (G), DST (FIST—level I) 657876570 (Grant No. SR/FIST/MS-I/2018/17), and Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17

A STABILITY CRITERION FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

In this paper, we prove that if a delay differential equation with impulse effects of the form x ′ (t) = A(t)x(t) + B(t)x(t − τ) , t � = θi, ∆x(θi) = Cix(θi) + Dix(θi−j), i ∈ N, verifies a Perron condition then its trivial solution is uniformly asymptotically stable

Global exponential stability for a class of impulsive BAM neural networks with distributed delays

In this paper, the exponential stability is investigated for a class of BAM neural networks with distributed delays and nonlinear impulsive operators. By using Lyapunov functions and applying the Razumikhin technique, delay–independent sufficient conditions ensuring the global exponential stability of equilibrium points are derived. These results can easily be utilized to design and verify globally stable networks. An illustrative example is given to demonstrate the effectiveness of the obtained results

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.The article has been written with the joint partial financial support of SERB-EEQ/2019/000365, RUSA-Phase 2.0 grant sanctioned vide letter No. F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No. F.510/8/DRS-I/2016(SAP-I) and DST (FIST-Phase I) vide letter No. SR/FIST/MS-I/2018-17, DST-PURSE 2nd Phase programme vide letter No. SR/ PURSE Phase 2/38 (G), the National Science Centre in Poland Grant DEC-2017/25/B/ST7/02888 and J. Alzabut would like to thank Prince Sultan University for supporting this work through research group Nonlinear Analysis Methods in Applied Mathematics (NAMAM) group number RG-DES-2017-01-17

O(t−β) -Synchronization and Asymptotic Synchronization of Delayed Fractional Order Neural Networks

This article explores the O(t−β) synchronization and asymptotic synchronization for fractional order BAM neural networks (FBAMNNs) with discrete delays, distributed delays and non-identical perturbations. By designing a state feedback control law and a new kind of fractional order Lyapunov functional, a new set of algebraic sufficient conditions are derived to guarantee the O(t−β) Synchronization and asymptotic synchronization of the considered FBAMNNs model; this can easily be evaluated without using a MATLAB LMI control toolbox. Finally, two numerical examples, along with the simulation results, illustrate the correctness and viability of the exhibited synchronization results