Taghreed A. Assiri

This article examines the analytical solution for Burger’s equations utilizing MADM and AHPMTM. We compare both analytical methods for convergence. The MADM uses a novel integral transform (the Mohand transform) with the Adomian decomposition method. The MADM solves the proposed problem using series form solutions that quickly converge to the exact solu-tions. The homotopy process with Mohand transformed and accelerated He’s polynomials underlie the novel AHPMTM approach to accelerate the convergence of the homotopy perturbation Mohand transform method (HPMTM). We compare solutions for MADM and AHPMTM to an exact solution. The methodology can be applied to different models in applied sciences and technology.

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach’s accuracy and utility, and it is presented in symmetric forms.

Simulation and numerical study for the blood ethanol concentration system (BECS) and the Lotka-Volterra system, i.e., predator-prey equations (PPEs) (both of fractional order in the Caputo sense) by employing a development accurate variational iteration method are presented in this work. By assessing the absolute error, and the residual error function, we can confirm the given procedure is effective and accurate. The outcomes demonstrate that the proposed technique is a suitable tool for simulating such models and can be extended to simulate other models.

This paper presents an optimal control problem of the general variable-order fractional delay model of advertising procedure. The problem describes the flow of the clients from the unaware people group to the conscious or bought band. The new formulation generalizes the model that proposed by Muller. Two control variables are considered to increase the number of customers who purchased the products. An efficient nonstandard difference approach is used to study numerically the behavior of the solution of the mentioned problem. Properties of the proposed system were introduced analytically and numerically. The proposed difference schema maintains the properties of the analytic solutions as boundedness and the positivity. Numerical examples, for testing the applicability of the utilized method and to show the simplicity, accuracy and efficiency of this approximation approach, are presented with some comprising with standard difference methods.