International Journal of Differential Equations

In this paper, the effects of magnetic field, thermal radiation, buoyancy force, and internal heat generation on the laminar boundary layer flow about a vertical plate in the presence of a convective surface boundary condition have been investigated. In the analysis, it is assumed that the left surface of the plate is in contact with a hot fluid, whereas a stream of cold fluid flows steadily over the right surface, and the heat source decays exponentially outwards from the surface of the plate. The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. The variations of fluid velocity and surface temperature for different values of the Grashof number, magnetic parameter, Prandtl number, internal heat generation parameter, Biot number, and radiation absorption parameter are tabulated, graphed, and interpreted in physical terms. A comparison with previously published results on similar special cases of the problem shows an excellent agreement.

In this paper, we aim to investigate optimal control to a new mathematical model that describes agree-disagree opinions during polls, which we presented and analyzed in Bidah et al., 2020. We first present the model and recall its different compartments. We formulate the optimal control problem by supplementing our model with a objective functional. Optimal control strategies are proposed to reduce the number of disagreeing people and the cost of interventions. We prove the existence of solutions to the control problem, we employ Pontryagin’s maximum principle to find the necessary conditions for the existence of the optimal controls, and Runge–Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system, and we perform numerical simulations using various initial conditions and parameters to investigate several scenarios. Finally, a global sensitivity analysis is carried out based on the partial rank correlation coefficient method and the Latin hypercube sampling to study the influence of various parameters on the objective functional and to identify the most influential parameters.

Our aim in this paper is to investigate the existence, uniqueness, and Mittag–Leffler–Ulam stability results for a Cauchy problem involving -Caputo fractional derivative with positive constant coefficient in Banach and Fréchet Spaces. The techniques used are a variety of tools for functional analysis. More specifically, we apply Weissinger’s fixed point theorem and Banach contraction principle with respect to the Chebyshev and Bielecki norms to obtain the uniqueness of solution on bounded and unbounded domains in a Banach space. However, a new fixed point theorem with respect to Meir–Keeler condensing operators combined with the technique of Hausdorff measure of noncompactness is used to investigate the existence of a solution in Banach spaces. After that, by means of new generalizations of Grönwall’s inequality, the Mittag–Leffler–Ulam stability of the proposed problem is studied on a compact interval. Meanwhile, an extension of the well-known Darbo’s fixed point theorem in Fréchet spaces associated with the concept of measures of noncompactness is applied to obtain the existence results for the problem at hand. Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems.

The World Health Organization declared that the total number of confirmed cases tested positive for SARS‐CoV‐2, affecting 210 countries, exceeded 3 million on 29 April 2020, with more than 207,973 deaths. In order to end the global COVID‐19 pandemic, public authorities have put in place multiple strategies like testing, contact tracing, and social distancing. Predictive mathematical models for epidemics are fundamental to understand the development of the epidemic and to plan effective control strategies. Some hosts may carry SARS‐CoV‐2 and transmit it to others, yet display no symptoms themselves. We propose applying a model (SELIAHRD) taking in consideration the number of asymptomatic infected people. The SELIAHRD model consists of eight stages: Susceptible, Exposed, Latent, Symptomatic Infected, Asymptomatic Infected, Hospitalized, Recovered, and Dead. The asymptomatic carriers contribute to the spread of disease, but go largely undetected and can therefore undermine efforts to control transmission. The simulation of possible scenarios of the implementation of social distancing shows that if we rigorously follow the social distancing rule then the healthcare system will not be overloaded.

The aim of this paper is to study a boundary value problem of the hybrid differential equation with linear and nonlinear perturbations. It generalizes the existing problem of second type. The existence result is constructed using the Leray–Schauder alternative, and the uniqueness is guaranteed by Banach’s fixed-point theorem. Towards the end of this paper, an example is provided to illustrate the obtained results.

In this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity, and shape of the boundary surface, we get variational formulation. The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. For the case of boundary conditions including the static pressure and stress, we prove that if the data of the problem are small enough and compatibility conditions at the initial instance are satisfied, then there exists a unique solution on the given interval. For the case of boundary conditions including the total pressure and total stress, we prove the existence of a solution without restriction on the data and parameters of the problem.