Browsing by Author "Bouakkaz , Ahlème"

Now showing 1 - 4 of 4
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    Existence, uniqueness and stability of solutions to a delay hematopoiesis model
    (Journal of Innovative Applied Mathematics and Computational Sciences , 2(2) , 23–30, 2022) Bouakkaz , Ahlème; Khemis , Rabah
    This work aims to investigate a delay hematopoiesis model where the delay depends on both the time and the current density of mature blood cells. Based on the Banach contraction principle, the Schauder’s fixed point theorem and some properties of a Green’s function, we establish several interesting existence and uniqueness results of positive periodic solutions for the proposed model. The derived results are new and generalize some previous studies. Keywords: Fixed point theorem, Green’s function, Mackey–Glass equation, Periodic solution, Positive solution.
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    Existence, uniqueness and stability results of an iterative survival model of red blood cells with a delayed nonlinear harvesting term
    (Journal of Mathematical Modeling Vol. 10, No. 3, pp. 515-528, 2022) Khemis , Marwa ; Bouakkaz , Ahlème; Khemis , Rabah
    In this article, a first-order iterative Lasota–Wazewska model with a nonlinear delayed harvesting term is discussed. Some sufficient conditions are derived for proving the existence, uniqueness and continuous dependence on parameters of positive periodic solutions with the help of Krasnoselskii’s and Banach fixed point theorems along with the Green’s functions method. Besides, at the end of this work, three examples are provided to show the accuracy of the conditions of our theoretical findings which are completely innovative and complementary to some earlier publications in the literature
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    MATHEMATICS 2 : solved Exercices : for first year university students in matter sciences and related disciplines.
    (Faculty of Sciences, 2025) Bouakkaz , Ahlème
    The more you practice mathematics, the more proficient you become just like with any other skill. Mastering a mathematics course, how- ever, goes beyond the rote memorization of rules, laws, and theorems. It prioritizes a deep understanding of the underlying concepts through consis- tent problem-solving, the application of various techniques, and the use of logical reasoning. This handout presents a collection of solved mathematical exercises in- tended for first-year undergraduate students in Matter Sciences (SM). Its primary aim is to provide students with a solid foundation while fostering rigorous scientific reasoning, thereby helping them master key concepts and better understand physical and chemical laws, phenomena, and models especially those that are often challenging to grasp. The document addresses key topics in analysis and linear algebra as out- lined in the Mathematics 2 syllabus. It is structured into four chapters: Chapters 1, 3, and 4 focus on concepts from analysis, while Chapter 2 con- centrates on topics from linear algebra. Each chapter begins with a brief overview of the main notions, followed by a set of fully solved exercises designed to reinforce learning through guided practice and problem-solving. Chapter 1 deals with solving first- and second-order linear ordinary dif- ferential equations using different methods such as the integrating factor method and variation of parameters. Chapter 2 focuses on linear algebra, emphasizing matrices, determinants, diagonalization, and systems of linear equations. Chapter 3 includes exercises with detailed solutions on Taylor series ex- pansions. Chapter 4 presents problems involving differential operators, as well as limits and partial derivatives of functions of two variables. The methodology employed here aims to encourage active learning, strengthen mathematical rigor, and bridge theoretical understanding with practical ap- plications. The detailed table of contents at the beginning of the document enables students to navigate the material efficiently and locate specific topics as needed.
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    New results on periodic solutions for a nonlinear fourth-order iterative differential equation
    (Journal of Prime Research in Mathematics, 18(2) , 88–99, 2022) Khemis , Rabah; Bouakkaz , Ahlème
    The key task of this paper is to investigate a nonlinear fourth-order delay differential equation. By virtue of the fixed point theory and the Green’s functions method, we establish some new results on the existence, uniqueness and continuous dependence on parameters of periodic solutions. In addition, an example is given to corroborate the validity of our main results. Up to now, no work has been carried out on this topic. So, the findings of this paper are new and complement the available works in the literature to some degree.