mina bagherpoorfard

‎This paper aims to demonstrate the flexibility of mathematical models in analyzing carbon dioxide emissions and account for memory effects. ‎The use of real data amplifies the importance of this study‎. ‎This research focuses on developing a mathematical model utilizing fractional-order differential equations to represent carbon dioxide emissions stemming from the energy sector. By comparing simulation results with real-world data, it is determined that the fractional model exhibits superior accuracy when contrasted with the classical model‎. ‎Additionally‎, ‎an optimal control strategy is proposed to minimize the levels of carbon dioxide, CO2, and associated implementation costs‎. ‎The fractional optimal control problem is addressed through the utilization of an iterative algorithm‎, ‎ and the effectiveness of the model is verified by presenting comparative results.

Using adaptive mesh methods is one of the strategies to improve numerical solutions in time dependent partial differential equations. The moving mesh method is an adaptive mesh method, which, firstly does not need an increase in the number of mesh points, secondly reduces the concentration of points in the steady areas of the solutions that do not need a high degree of accuracy, and finally places the points in the areas, where a high degree of accuracy is needed. In this paper, we improved the numerical solutions for a three-phase model of avascular tumor growth by using the moving mesh method. The physical formulation of this model uses reaction-diffusion dynamics with the mass conservation law and appears in the format of the nonlinear system of partial differential equations based on the continuous density of three proliferating, quiescent, and necrotic cell categorizations. Our numerical results show more accurate numerical solutions, as compared to the corresponding fixed mesh method. Moreover, this method leads to the higher order of numerical convergence.