Volume 25, Issue 1

This study aims to analyze the finite-time stability performance of both non-delayed and delayed fractional-order neural networks. Our primary aim is to investigate the finite-time stability characteristics by introducing a novel inequality designed for estimating the settling time. This fresh inequality serves as the foundation for establishing sufficient criteria, formulated as linear matrix inequalities, which guarantee the finite-time stability of both non-delayed and delayed fractional-order neural networks. Additionally, we underscore the importance of incorporating comprehensive information regarding the lower and upper bounds of the activation function, especially in the context of the proposed non-delayed model. Unlike the previous works, in this paper, the linear matrix inequality technique has been adopted towards the finite-time stability behavior of the proposed model. At last, some numerical examples are examined to validate the efficacy and conservatism of the presented approach and established theoretical results over the existing literature.

Tuberculosis (TB) is caused by a bacterium called Mycobacterium tuberculosis (Mtb). When Mtb enters inside the pulmonary alveolus, it is phagocytosed by the alveolar macrophages, followed by a cascade of immune responses. This leads to the recruitment and accumulation of additional macrophages and T cells in the pulmonary tissues. A key outcome of this is the formation of granuloma, the hallmark of TB infection. In this paper, we develop a mathematical model of the evolution of granuloma by a system of partial differential equations that is based on the classical Keller–Segel chemotaxis equation. We investigate the effect of different parameters on the formation of granuloma. We present numerical simulation results that illustrate the impact of different parameters. The implication of our result on the disease progression is also discussed.

The effect of gravity-field modulation is investigated in a nano liquid-confined Hele-Shaw cell. This study aims to finish the work described in (S. N. Rai, B. S. Bhadauria, K. Anish, and B. K. Singh, “Thermal instability in nanoliquid under four types of magnetic-field modulation within Hele-Shaw cell,” Int. J. Heat Mass Transfer , vol. 145, no. 7, p. 072501, 2023) for oscillatory convection. The existence of the complex Ginzburg-Landau equation (CGLE) model is constrained by the requirement ω 2 > 0. The magnetic fluxes in the Hele-shaw cell are governed by CGLE with g-jitter. The quantity of heat-mass transfer is examined in the presence of a g-jitter. In addition, the findings of our research on transport analysis indicate that oscillatory mode is preferable to stationary mode. It is also found that the gravity-driven Hele-Shaw layer has lower transport properties. Further, the transport analysis is compared to previous research and shown to have improved results.

In this paper, we investigate the existence and uniqueness solutions for a fuzzy Neutral fractional integro-differential equation with non-local conditions. First, we show the existence of solutions with the help of the Non-linear alternative for one-value function, as well as Krasnoselskii’s and Banach’s fixed point theorems. Moreover, we examine the generalized Ulam Hyers (GUH) and Ulam Hyers Rassias stability for our main problem. Finally, an example is presented to show the usability of our major results.

In this paper, we propose a two-group deterministic COVID-19 model which takes into account educational campaigns and the fact that people infected with COVID-19 may choose either modern (allopathic) medicine, traditional medicine or may combine the two modes of treatment. The model is analysed in the case where modern medicine is the only mode of treatment and when traditional medicine is taken as an adjuvant (or another mode of treatment). We prove in the first case that the model has a disease-free equilibrium (DFE), globally asymptotically stable when the control reproduction number is less than one and whenever it is greater than one, we prove the local asymptotic stability of the endemic equilibrium. In the second case, we prove that, misconceptions in the population lead to a backward bifurcation phenomenon, which makes the control of the disease more difficult. We derive using the Lyapunov method that a threshold T $\mathcal{T}$ ensures the global asymptotic stability of DFE in some cases when its value is less than one. Both models are fitted using daily COVID-19 cumulative cases reported from January to February 2022 in South Africa. We found a control reproduction number less than one, meaning that COVID-19 will be eliminated. Comparison of the two models fits highlights that misconceptions should be taken into account to accurately describe the dynamics of COVID-19 in South Africa. Numerically, we prove that educational campaigns should focus on preventive measures and both traditional and allopathic medicine health care systems should complement each other in the fight against COVID-19.

This article studeis the nonlinear (2 + 1)-dimensional Zoomeron equation by utilizing the various prominent analytical approaches namely the unified method and the extended hyperbolic function approach. The analysis in the current paper demonstrates the presence of travelling wave solutions. The applied methods are utilized as powerful tools to investigate and solve the model. The results obtained through these analytical methods reveal insightful patterns in the behavior of the Zoomeron equation. The significance of our work lies in the uniqueness of the methods employed. The two methods are applied to systematically analyze the equation, revealing hidden patterns and structures within its solution space. This leads to the discovery of a collection of solitary wave solutions such as kink waves, singular kink waves, periodic waves and dark soliton using contour plots, 3D and 2D graphics. In this article, we definitely prove that as the free parameters change, the wave amplitude changes as well. It is shown that the applied strategies are more effective and may be implemented to a variety of contemporary nonlinear evolution models emerging in mathematical physics.