Nooraini Zainuddin

Distributed denial-of-service (DDoS) attacks have become a major threat to the stability of critical infrastructure networks, where even short service disruptions can lead to severe operational and economic consequences. To better capture the complex dynamics of these attacks, we extend an existing epidemic-based DDoS model by employing the fractal–fractional (FF) Atangana–Baleanu (AB) operator, which effectively accounts for memory effects, network heterogeneity, and irregular traffic patterns commonly observed in cyber environments. Within this framework, we establish the existence and uniqueness of solutions and examine the Ulam–Hyers stability of the proposed system. The local stability of both infection-free and endemic equilibria is assessed to identify the conditions under which the network can maintain normal operation. Numerical simulations are performed using the Adams–Bashforth method for various combinations of fractional and fractal orders. The results show that the FFAB formulation captures slower decay, extended memory, and more realistic transient dynamics than its classical counterpart. These findings demonstrate that incorporating FF dynamics offers a more flexible and accurate representation of DDoS propagation and quarantine based mitigation, providing valuable insights for enhancing the resilience of modern cyber-infrastructure systems.

Nonlinear least squares (NLS) models are extensively used as optimization frameworks in various scientific and engineering disciplines. This work proposes a novel structured conjugate gradient (SCG) method that incorporates a structured diagonal approximation for the second-order term of the Hessian, particularly designed for solving NLS problems. In addition, an acceleration scheme for the SCG method is proposed and analyzed. The global convergence properties of the proposed method are rigorously established under specific assumptions. Numerical experiments were conducted on large-scale NLS benchmark problems to evaluate the performance of the method. The outcome of these experiments indicates that the proposed method outperforms other approaches using the established performance metrics. Moreover, the developed approach is utilized to address the inverse kinematics challenge in controlling the motion of a robotic system with four degrees of freedom (4DOF).

HRMARS is well established journal publisher based in Pakistan. It is publishing prominent journals in social sciences since 2011.

Clustering is an important method in data analysis, faces challenges due to the different nature of datasets, resulting in certain algorithms being less effective and taking a long time. Choosing the most effective clustering method involves evaluating its accuracy and computational speed for a dataset poses a significant challenge for today's researchers. To address these issues, current study compares different clustering methods, by using datasets, including iris, seed, and well log to evaluate their accuracy and execution speed. Results show that K-means performs better with large datasets. As sample size increases, the accuracy of the K-means algorithm tends to improve. The execution time of k-means is influenced by the number of features in the dataset, with datasets having a larger number of features typically requiring more time to process. Mean shift algorithm and spectral clustering algorithm are performed well in small data sets, but it takes a long time.

Nonlinear least squares (NLS) problems are commonly encountered in a wide range of scientific and engineering fields, often demanding robust and efficient optimization methods for their solution. Traditional approaches for solving NLS problems frequently encounter difficulties related to high computational costs and memory usage, particularly in large-scale scenarios. This study introduces a novel structured Dai-Yuan two-term conjugate gradient (CG) method to address the minimization of NLS problems. By leveraging a Taylor series expansion of the objective function's Hessian, a structured vector approximation, representing a matrix-vector interaction, is constructed. This formulation adheres to a quasi-Newton condition. The method utilizes this structured approximation to enrich the conventional search direction with additional curvature information from the Hessian. The resulting search direction satisfies the required descent condition. Furthermore, numerical experiments on a range of benchmark problems demonstrate that the proposed method offers superior performance, outperforming several existing techniques.

In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.

The importance of thermal radiation impacts on electromagnetohydrodynamics (EMHD) hybrid nanofluid movement and heat transference towards stretching/shrinking surface is investigated. The influences of external effects such as suction, heat absorption and generation are also being considered. The hybrid nanofluid chosen for exploration is Graphene Oxide (GO) and Iron Oxide (Fe₃O₄) as nanoparticles, while water (H₂O) is a base fluid. The mathematical modelling in partial differential equations (PDEs) is formulated to ordinary differential equations (ODEs) for simplicity using an appropriate similarity variable. The solution of the reduced ODEs is then computed with the help of bvp4c solver built-in MATLAB software. The findings reveal that the magnetic field augmented the velocity profile, while thermal radiation affects the temperature profiles to amplify. The heat generation and absorption upsurged the heat transfer for GO-Fe₃O₄/H₂O with accompanying effects like plate thickness. It is also worth mentioning that GO-Fe₃O₄/H₂O enhanced skin friction and heat transfer by about 3.2% and 1.6%, respectively, more than Fe₃O₄/H₂O.

This study involves the investigation of convective boundary conditions and joule heating in a computational analysis of the electromagnetic hydrodynamic (EMHD) This study involves the investigation of convective boundary conditions and joule heating in a computational analysis of the electromagnetic hydrodynamic (EMHD)

In this study the new statistical method kernelized rank order (KROD) numerical solution is analyzed to convert non spherical data to spherical form using diffe In this study the new statistical method kernelized rank order (KROD) numerical solution is analyzed to convert non spherical data to spherical form using diffe

Obtaining the solutions of high-dimensional partial differential equations (PDEs) seems to be difficult by utilizing the classical numerical methods. Recently,