Pusat Pengajian Sains Matematik - Tesis
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- PublicationNumerical Approximations Of Time-Fractional Partial Differential Equations Based On B-Splines Collocation Methods(2025-09)Anya, Okeke AnthonyRecently, there has been an upsurge in the study of fractional partial differential equations (FPDEs). This is because FPDEs have numerous applications in engineering and science owing to their non-local properties. For instance, FPDEs have been employed to solve problems in the fields of physics, chemistry, biology, biochemistry, medicine, electron transportation, financial data, groundwater flow, and geo-hydrology. FPDEs are the generalizations of traditional partial differential equations. Exact analytical solutions for FPDEs are generally undetermined owing to their complicated nature. Thus, there is intense motivation to explore possibilities for developing efficient and reliable approximate analytical and numerical methods for solving FPDEs. This study focused on the development of efficient approximate numerical methods.
- PublicationMulti-Stage Differential Transform Methodforsolving Classical And Fractional Differential Algebraic Systems(2025-09)Alahmad, Khalil IbrahimDifferential equations are known as a mathematical method to model a problem that exists in science, chemistry, physics and economics. Generally, systems of differential equations can be classified into systems of fractional differential algebraic equations and systems of differential algebraic equations. Fractional differential algebraic equations and differential algebraic equations have been used to model complex systems in various fields, but the traditional numerical solution methods used often struggle with their solution behavior. The objective of this research is to develop two techniques to solve a system of fractional differential algebraic equations as well as a system of differential algebraic equations based on initial value problems through the standard differential transformation method and the fractional differential transformation method.
- PublicationDynamical Behaviour Of Prey-Predator Systems: Exploring Herd Mechanisms, Prey Refuges, And The Dispersal Process(2025-09)Manaf, Zati Iwani AbdulThe complex interactions between prey and predator dynamics are a central concern in ecology, influencing both biodiversity and ecosystem stability. This thesis addresses relatively underexplored aspects of these interactions by investigating the effects of three crucial ecological mechanisms: herd mechanism, prey refuges, and dispersal processes. The primary objective is to analyse how prey-predator systems respond to the presence and absence of these factors. To achieve this, an analysis of four existing ecological ordinary differential equation (ode) models is conducted, focusing on prey-predator systems characterised by type ii and square-root functional responses. Based on these analyses, three new ecological models are proposed. The first model uniquely incorporates herd behaviour exclusively in predator populations, directly addressing the literature gap on predator herding. The second model extends this by incorporating prey refuge effects to explore their joint influence with predator herding. The third model further extends the prey-predator model with predator herd behaviours into a partial differential equation (pde) system, enabling the examination of spatial and dispersal process in this ecological system.
- PublicationReaction System Ranks For Union-Additive Functions Under Various Resource Constraints And Their Hierarchical Analysis(2025-09)Husain, IntekhabReaction systems, introduced nearly two decades ago by Ehrenfeucht and Rozenberg, are a robust modeling framework inspired by the complex chemical interactions within living cells. A key aspect of reaction systems is the associated rs function, which describes the transition of states in an interactive process. Mathematical studies of rs functions have garnered significant interest, particularly focusing on functions specified by minimal reaction systems. The concept of reaction system rank is evolving as a significant research topic; it measures the complexity of an rs function based on the smallest set of reactions that can specify it. This work studies the reaction system ranks of functions belonging to the class of union-additive rs functions, F𝑈 (𝑆), introduced by Salomaa.
- PublicationG-Type Random 3 Satisfiability With Discrete Hopfield Neural Network(2025-09)Gao, YuanLogical relationships are crucial in artificial intelligence, especially in structuring data relations, as logical relationships provide a structured and formal framework. However, existing models often overlook the potential for flexible representations in satisfiability logical rules. To address this, this thesis proposes a novel logical rule called G-type Random 3 Satisfiability. This rule combines high-order, systematic, and non systematic logic to create a logical framework with high randomness and flexibility. When embedded into Discrete Hopfield neural networks, this logical rule significantly enhances the adaptability of the network in associative memory and complex logical task processing. To improve training efficiency, a novel Binary Optimal Solution Ant Colony Optimization algorithm is introduced as the learning mechanism. By refining the initialization process and update rules, the algorithm achieves a significantly faster convergence speed. For the retrieval phase, a new mutation strategy called Randomized Pairwise-Single Mutation is proposed, which enhances global solution diversity and further optimizes the quality of retrieval results.