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.

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.

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.

In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter $\sigma$ is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor $\Theta$. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study; the results obtained by the proposed method are more stable than previous research in this area.

This research paper study the existence, uniqueness and Ulam–Hyers stability of the solutions of a certain system of thegeneralized Caputo fractional differential equations in the context of the generalized metric spaces. The existence and uniqueness theorems are proved by using the Krasnoselskii’s and Perov’s fixed point theorems under the Bielecki norm with a Lipschitzian matrix in the generalized metric spaces. Moreover, the Ulam–Hyers stability analysis is conducted based on the Urs’s criterion. An example, lastly, is proposed to check the efficiency of the above-mentioned theorems. The results are novel and provide extensions to some of the findings known in the literature.

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.