2- رياضيات
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Item Mathematical Modeling and Analysis of Malaria Propagation(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) BOUGHRARA, AssiaThe 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.Item Analytical and Numerical Analysis of A Generalized Non Standard Volterra Integro-Differential Equations(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) 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.Item Control methods for inverse problems(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) ALI, LindaIn 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 .Item A common fixed point theorem and its application in dynamic programming(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) CHENIKHAR, SafaThis 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.Item Limitit cycles for certain differential systems formed by hamiltonian systems(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) MOUELLAH, BoumedieneIn this work, we show a new way of using the averaging theory of first order for studying families of periodic orbits in the extension of the Van der Pol oscillator to a Hamiltonian system of the form (1 ) , 2 , (1 ) , , 2 2 y y x y x y p x x p p y xyp y p x y x p where px and py are the conjugate momenta of the variables x and y , respectively and is a small parameter. In the second part of this work, we provide the maximum number of limit cycles for continuous and discontinuous planar piecewise differential systems formed by linear Hamiltonian saddles and separated either by one or two parallel straight lines.Item Mathematical Analysis of double-age structured model(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06) BELGHIT, MalakThis thesis highlights the importance of age-structured mathematical models in understanding the behavior of complex infectious diseases. The studied model illustrates how temporal factors such as biological age and incubation period affect the spread of infection, and demonstrates the possibility of controlling epidemic dynamics through effective intervention strategies. The results show that targeted vaccination can significantly reduce the spread of the disease, reinforcing the role of mathematical modeling in supporting scientifically based public health decisions.Item Existence of positive solutions for double-phase problem(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) NECIB, MerayaIn this work, we discuss the existence of positive solutions of a class of differential equations called double phase with Dirichlet condition, that involves both a singular and a superlinear parametric term, posed by the discontinuous weights and the the structure of the differential operator. Using Nehari’s method and critical point theory, it is shown that for small values of the argument of the parameter λ, the equation admits at least two positive solutions.Item Synchronization of Chaos in Discrete Dynamical Systems(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) RADJAI, AbdelbariThe objective of this thesis is to present the problem of chaos synchronization. More specifically, we are interested in the synchronization of discrete nonlinear dynamical sys- tems, whose formulations are given by recurrent functions with the presence of bifurcation parameters, where a small perturbation in the initial conditions results in a large discrep- ancy between long-term observations. The unification of observations of two long-term phenomena is equivalent to the syn- chronization of their representative dynamical systems from a certain rank (time) by applying the various types of synchronization cited in the literature, including Com- plete Synchronization, Anti-Synchronization, Phase Synchronization, Lag Synchroniza- tion, Generalized Synchronization, Projective Synchronization, FSHP Synchronization, and Q-S Synchronization.Item Reproducing Kernel Hilbert Space Method For Solving Fractional Integro-Differential Systems(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) KRAIDIA, IsraThis dissertation develops an efficient numerical method for solving fractional integro differential systems involving the Caputo fractional derivative. The proposed approach employs the Reproducing Kernel Hilbert Space (RKHS) method to construct ap proximate solutions expressed as uniformly convergent series, ensuring both high accuracy and rapid convergence. Numerical examples demonstrate the effectiveness and precision of the RKHS method in addressing complex fractional systems. The results reveal the significant impact of the fractional derivative order on the qualitative behavior of the solu tions, underscoring the importance of fractional calculus in modeling memory-dependent phenomena. This study establishes the RKHS method as a robust and promising tool for the numerical analysis of fractional systems. Future work may extend this framework to incorporate other types of fractional derivatives, higher-dimensional problems, and systems with more intricate initial and boundary conditionsItem On the stability of the willamowsky-Rossler chaotic reaction diffusion model(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) SLIMI, KarimaThe study of dynamical systems is a fundamental topic in the natural and engineering sciences, contributing to understanding the behavior of complex systems and analyzing their stability. In this study, we will analyze a dynamical system containing six equilibria, with the aim of classifying the system's parameter regions based on the presence of these equilibria and determining their stability conditions. We will use the Lyapunov method to analyze local and global stability, and evaluate the presence of a Hopf bifurcation at a particular equilibrium point in the Wilamowski-Rössler system. In addition, we will discuss the study of interaction propagation in three- dimensional systems and global asymptotic stability in the partial differential equations (PDEs) representing these systems. This study aims to achieve a deeper understanding of the system's dynamics and determine the stability conditions of its equilibria, contributing to the development of knowledge in the field of dynamical systems and their applications.Item Methods for studying blow-up phenomena in differential equations(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-03) LASSOUED, HamzaThis thesis investigates the dynamics of a coupled nonlinear wave system with internal fractional damping, a model relevant to viscoelastic materials and engineering ap- plications. The study focuses on two key aspects: establishing the local existence and uniqueness of solutions and analyzing conditions leading to finite-time blow-up. Employing functional analysis and C0-semigroup theory, we reformulate the system as an abstract evo- lution equation in a Hilbert space, proving local well-posedness under specific conditions on the nonlinear exponents. A carefully designed Lyapunov functional is used to derive criteria for solution blow-up, highlighting the interplay between nonlinearity and fractional damp- ing. The results contribute to the theoretical understanding of fractional partial differential equations and offer insights for practical applications, such as vibration control and material stability. This work advances the mathematical framework for nonlocal systems and lays the groundwork for future research into global existence and numerical simulations.Item General decay for a viscoelastic wave equation of the Kirchhoff type with delay(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) MESLOUB, IkramThe main goal of this thesis is studing the Asymptotic behavior of solutions to a vis- coelastic Kirchhoff-type plate equation with memory and delay terms, under classical initial and boundary conditions.first we present necessary mathematical preliminaries. Then,by using energy estimates and suitable assumptions on the damping and relaxation functions, we prove the global existence. Finally, we establish a general decay result for the total energy by con- structing an appropriate Lyapunov functional. The result shows that the energy decays over time, illustrating the combined stabilizing effect of damping and memory, even in the presence of delay.Item Chaos and Bifurcations in some Zeraoulia-Sprott mappings(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) HABHOUB, NassimaThe main goal of this thesis is to investigate different kinds of bifurcations in some 2-D Zeraoulia-Sprott chaotic discrete mappings. It exoplores the normal form of these systems, the various kinds of bifurcations, and the conditions under which they occur. the study also inverstigates chaos and bifurcation phenomena in both the modified Lozi and Logistic systems highlighting the main characteristics of each system.Item On the Drazin inverse and generalized Drazin inverse of an operator and its applications(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) FAR, AyaThis thesis aims to study the Drazin inverse of bounded linear operators in Banach spaces, focusing on its algebraic and spectral properties, as well as its applications in solving differential equations and linear systems. The thesis is divided into four chapters: • Chapter 1: Preliminaries Covers fundamental concepts such as linear operators, spectrum, ascent and de- scent, and the Riesz projection. • Chapter 2: Drazin Inverse Defines the Drazin inverse, conditions for its existence, its relation to the spectrum, and special cases. • Chapter 3: Generalized Drazin Inverse Involves operator decomposition, additional spectral properties, and key partial order relations. • Chapter 4: Applications Uses the Drazin inverse to solve differential equations and demonstrates computa- tional methods with illustrative examples. The thesis highlights the importance of the Drazin inverse in extending the concept of invertibility and providing effective analytical tools for linear systems in applied mathe- matics.Item Asymptotic stability and explosion of solutions for a class of hyperbolic problem with delay time.(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) SLIMANI, OuidadIn this work, we investigated the stability of solutions using the energy method, and finite time blow-up of solutions through a direct approach based on Lyapunov functionals, for certain classes of nonlinear evolution equations. First, the theoretical concepts and methodological tools introduced in this study provide a foundational framework for the detailed results and analyses presented in the subsequent chapters. Next, we established the asymptotic stability of the solution to a Kirchhoff type viscoelastic wave equation that includes Balakrishnan Taylor damping and a time delay term. By constructing an appropriate Lyapunov functional, employing differential inequalities, we proved that the total energy of the system decays to zero over time, despite the additional complexity introduced by the memory and delay effects. Finally, we examined the finite time blow up of solutions for a problem involving a time delay term. Our objective was to determine sufficient conditions under which the solution either decays to zero as time approaches infinity or blows up in finite time, depending on the interplay between the source and damping terms in the evolution equation. From our literature review, we observed that classical models often incorporate nonlinear damping and first order perturbation terms, both of which have been extensively studied.Item Acceleration of the convergence of the gradient method by using the conjugate gradient(University Larbi Tébessi – Tébessa, 2024-06-09) BAHI, AminaThe conjugate gradient method is considered one of the most important methods used to speed up the gradient algorithm, for this purpose, several related algorithms have been developed. We will present a new method that accelerates the convergence of the gradient method (the higher slope method) using a new version of the conjugate gradient and a powerful non-exact linear Wolf search. It will be shown that this algorithm generates descent trends and converges globally.Item STUDY OF EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS OF SOME SYSTEMS AND PARTIAL DIFFERENTIAL EQUATIONS(University Larbi Tébessi – Tébessa, 2024-06-09) SAKHER, IlhamIn this work we are concerned to prove the existence, uniqueness and the continuous dependance of a strong solution upon the data of some mixed problems with classical ( Dirichlet, Neumann) and integral conditions for a hyperbolic class of equations and for a hyperbolic system. In a first case, we treate a mixed problem with purely classical conditions and in a second case we combine a classical and an integral condition. In our proofs, we use functionnal analysis method.Item Stability Results of a Coupled Wave Equations With Time Delay(University Larbi Tébessi – Tébessa, 2024-06-09) ZERDOUMI, NabilaThe aim of this work is to give a results related to locally coupled wave equations with non- smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay (studied by Mohammad Akil et al[1]). The research aims to study the existence and uniqueness of solutions under appropriate assumptions using semigroup theory. Using a general criterion of Arendt-Batty, we show the strong stability of our system in the absence of the compactness of the resolvent.Item On some q-transformations(University Larbi Tébessi – Tébessa, 2024-06-08) AZRI, Dhia EddineThis dissertation deals with the most important definitions and mathematical prop- erties of q-calculus, such as quantum derivative and Jackson integration, in addition to formulating quantum transformations such as q-Laplace transform and q-Mellin trans- form.Item Classical Numbers defined by Generating functions(University Larbi Tébessi – Tébessa, 2024-06-08) BRAHMI, Chihab EddineThe main object of this dissertation is to investigate some classical numbers using the corresponding Generating functions .For each sequence included in this dissertation, we shall provide an overview About its construction as well as some of its applications. Among classical numbers, we proposed Fibonacci, Lucas, Pell, Bell, Harmonic, Stirling both the first and second kind,...among others