2- رياضيات

Mathematical Modeling and Analysis of Malaria Propagation

2025-12-02T09:46:52Z

Mathematical Modeling and Analysis of Malaria Propagation BOUGHRARA, Assia The aim of this thesis is to study the dynamics model of the malaria parasite. The mathematical model was developed based on the SEIR model for humans and the SI model for mosquitoes. The basic reproduction number was calculated, and then the stability of the disease-free equilibrium point was studied. If R0>1, it is unstable, but if R0<1, it is locally asymptotically stable. This was proven using the Poincaré-Lyapunov theorem and globally asymptotically stable. This was proven using the Lyapunov function. The existence and uniqueness of the endemic equilibrium point were studied, and it was proven to be globally asymptotically stable if R0>1, also using the Lyapunov function, and otherwise unstable.

Analytical and Numerical Analysis of A Generalized Non Standard Volterra Integro-Differential Equations

2025-12-02T08:54:50Z

Analytical and Numerical Analysis of A Generalized Non Standard Volterra Integro-Differential Equations KHALED, Soumia • Fredholm and Volterra integral equations hold a significant position in mathe- matics due to their wide-ranging applications across various scientific fields. • In this thesis, we focus on a specific form of the non linear, non standard, integro-differential Volterra equation. • Using Schauder fixed point theorem, we establish the existence and unique- ness for the solution of this integro-differential Volterra equation under well-defined conditions. • We then apply the Fibonacci Wavelet Collocation method to obtain an approximate solution to this integro-differential equation, followed by illustrative examples demonstrating the obtained results.

Control methods for inverse problems

2025-11-17T09:28:12Z

Control methods for inverse problems ALI, Linda In this memory, we have made a detailed study of the inverse problem and in particular the observation problem and analyzed an epidemiological model of the type SIS using optimal con- trol methods with the aim of identifying unknown coefficients such as transition and recovery coefficients . The inverse problem is transformed into an optimal control problem in which a cost function is defined that minimizes the difference between the model results and the observed data at the final time and is often represented by differential or integral equations, where the results of the theory such as existence and necessary conditions for optimality are proved .

A common fixed point theorem and its application in dynamic programming

2025-11-17T07:59:02Z

A common fixed point theorem and its application in dynamic programming CHENIKHAR, Safa This master’s thesis establishes a significant common fixed point theorem for four self-mappings defined on complete metric spaces, under the assumptions of weak compatibility and a gener- alized Φ-contraction condition. This contribution extends and generalizes previous results in fixed point theory, demonstrating its applicability by solving functional equations that arise in dynamic programming. These equations typically represent recursive formulations of optimal value functions in multistage decision processes. The authors construct a comprehensive framework using metric fixed-point tools, ensuring the existence and uniqueness of solutions to these functional systems. An illustrative example to confirm the theoretical assumptions. This contribution effectively bridges abstract fixed-point theory with applied optimization and control problems, enriching the mathematical foundation of dynamic programming models and opening avenues for further research in optimization.