Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo–Fabrizio derivative

This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo–Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard’s iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian’s decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.

Mathematical analysis of tuberculosis control model using nonsingular kernel type Caputo derivative

This research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.

The Effects of Ear Dimensions and Product Attributes on the Wearing Comfort of Wireless Earphones

The purpose of this study was to evaluate the wearing comfort of wireless earphones. In order to test the effects of ear dimensions with the product characteristics on wearing comfort, first, a total of six ear dimensions were selected. In addition, each ear dimension was classified into two groups using K-means clustering analysis. Second, four major factors related to wearing comfort (pain, pressure, comfort, and fixation) with four sample products were investigated, considering the characteristics of the product (kernel-type/open-type), operation method (touch-input/button-press), and shape. Finally, a total of 38 participants (23 men and 15 women) participated in the experiments. The results show that pain in the ear canal was low to the participants who had a long length of the ear canal–incisura intertragica, and the fixation of the ear canal was high in the participants with a long incisura intertragica–antitragus cluster. Compared to open-type products, kernel-type products put more pressure on the ear canal area, so the participants felt less comfortable. In terms of operation methods, operating products in touch-input types caused less pain than operating products in button-press types did. Overall, the factors affecting user satisfaction and wearing comfort determined in this study will serve as a basis for the future design of wireless earphone products.

Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

In this article, we provided a numerical simulation for asymptotic normality of a kernel type estimator for the intensity obtained as a product of a periodic function with the power trend function of a nonhomogeneous Poisson Process. The aim of this simulation is to observe how convergence the variance and bias of the estimator. The simulation shows that the larger the value of power function in intensity function, it is required the length of the observation interval to obtain the convergent of the estimator.

Existence theory and approximate solution to prey–predator coupled system involving nonsingular kernel type derivative

This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent example of prey–predator system, we support our results. Some graphical presentations are given using Matlab.