numerical simulations

Timoshenko's problem is not a recent problem and many articles exist concerning his study.  New physical problems appear and require a good mathematical understanding of the behavior of this phenomenon.  Our contribution will consist in studying the numerical stability of a Timoshenko system with second sound.  We introduce a finite element approximation and prove that the associated discrete energy decreases and we establish a priori error estimates.  Finally, some numerical simulations are obtained.

In this paper, we consider the Moore–Gibson–Thompson–Fourier system made by coupling the Moore–Gibson–Thompson (MGT) equation with the classical Fourier heat equation known as the MGT–Fourier model.  For $\sigma=\alpha\beta-\gamma>0$, the authors used the semi-group method to prove the existence and uniqueness of global solutions and the exponential stability of total energy.  Our contribution will consist in studying numerical method based on finite element discretization in the spacial variable $x$ and finite difference schema in time of the MGT–Fourier model.  A d

Catalytic action is one of the most important characteristics of enzymes in chemical reactions.  In this article, we propose and study a mathematical model of chemical kinetic reaction with the memory effect using the new generalized Hattaf fractional derivative.  The existence and uniqueness of the solutions are established by means of fixed point theory and, finally, to support the theoretical results, we end the article with the results of numerical simulations based on a novel numerical scheme that includes the Euler method.

Scale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents.  These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant.  Mealybugs feed on the sap of plants, drying them out and discoloring them.  In this research, we propose and investigate a fractional model for the transmission of the Cochineal.  In the first place, we prove the positivity and boundedness of solutions i

This paper deals with a fractional optimal control problem model that describes the interactions between hepatitis B virus (HBV) with HBV DNA-containing capsids, liver cells (hepatocytes), and the cytotoxic T-cell immune response.  Optimal controls represent the effectiveness of drug therapy in inhibiting viral production and preventing new infections.  The optimality system is derived and solved numerically.  Our results also show that optimal treatment strategies reduce viral load and increase the number of uninfected cells, which improves the patient's quality of lif

In this work, we formulate a model describing the growth of a pest population with seasonal diapause at the larval stage.  The model includes the insect resistance to chemical treatments and their adaptation against a hostile environment.