Abstract

This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized using three B-splines-cubic, cubic trigonometric and extended cubic B-splines-while temporal discretization is handled by a finite difference scheme. The proposed schemes are rigorously analyzed for stability and convergence. Their performance is evaluated in terms of accuracy and computational efficiency. Numerical experiments confirm the effectiveness of these techniques in capturing the dynamics of the fractional NWS equation. Each B-spline variant demonstrates unique strengths, highlighting the flexibility of B-spline approaches for solving fractional differential equations with nonlocal, memory-dependent operators. These results affirm the reliability and robustness of B-spline-based methods for such problems, paving the way for future advancements in this area.OPEN ACCESS Received: 23/08/2025 Accepted: 08/12/2025 Published: 16/04/2026

Abstract

This paper presents an enhanced Least Squares Support Vector Machine (LS-SVM) approach for meshless and accurate solution of higher-order boundary value problems (BVPs) that commonly arise in structural mechanics, fluid dynamics, and other engineering fields. The discussed method formulates thirdand fourth-order linear and nonlinear ordinary differential equations (ODEs) as data-driven optimization problems, eliminating the need for traditional mesh-based discretization. Leveraging a Radial Basis Function (RBF) kernel and regularization-based control of model complexity, the LS-SVM captures complex solution behaviour while maintaining stability and smoothness. The meshless nature of the model ensures geometry-independence, making it suitable for irregular or multi-point boundary conditions. A comparative analysis with established machine learning techniques, including Ridge Regression (RR), classical SVM, Random Forest (RF), and Extreme Gradient Boosting (XGB), demonstrates the competitive accuracy, robustness, and efficiency of LSSVM. The results highlight its potential as a promising solver for nonlinear and multi-point problems where meshless methods are advantageous. The results highlight its potential as a promising solver for simulation-based workflows in computational mechanics and scientific computing, where adaptability, generalization, and reliability are critical.OPEN ACCESS Received: 25/08/2025 Accepted: 21/10/2025 Published: 16/04/2026

Abstract

This paper introduces a new design for a permanent magnet motor (PMM) tailored for automotive steering applications. By utilizing new permanent magnet topology, high-performance materials, and rotor designs, the newly proposed PMM design reduces torque ripple while boosting torque density. This design is integrated within a sophisticated steer-bywire (SBW) system, enabling seamless operation and reliable feedback, which are crucial for modern vehicles. The finite element analysis (FEA) substantiates the effectiveness of the proposed PMM, resulting in a 1.2% enhancement in magnetic flux density, a 4.65% increase in static torque, and a 4.4% reduction in torque ripple. This research addresses the issues in wheel steering technology and lays the groundwork for future automotive motor technologies. And also, it provides valuable insights into the development of automotive technologies, paving the way for enhanced performance and sustainability in the automotive sector. Furthermore, these improvements not only aim to enhance driver satisfaction but also align with the industry’s transition toward greener technologies.OPEN ACCESS Received: 05/10/2025 Accepted: 15/12/2025 Published: 16/04/2026

Abstract

This paper establishes a comprehensive analysis of a coupled system of nonlinear Hadamard-type fractional differential equations subject to generalized nonlocal integral boundary conditions. The distinct logarithmic kernel of the Hadamard derivative makes this framework particularly suitable for modeling scale-invariant processes and ultraslow diffusion phenomena. The existence and uniqueness of solutions are rigorously investigated using fixed point theory: Banach’s contraction principle ensures uniqueness, while the Leray-Schauder nonlinear alternative guarantees existence under more general growth conditions. Furthermore, the system is proven to be Ulam-Hyers stable, ensuring that approximate solutions remain close to exact solutions, which is crucial for the robustness of the model in practical applications. The theoretical findings are effectively validated through two detailed numerical examples, demonstrating the applicability of the established results to different classes of nonlinearities.OPEN ACCESS Received: 22/08/2025 Accepted: 03/11/2025 Published: 23/01/2026

Abstract

This paper presents a rigorous framework for generalizing Laguerre polynomials to the fractional domain using the Caputo derivative. We solve the resulting fractional Laguerre differential equation via the power series method, deriving an explicit formfor the fractional Laguerre functions. A key contribution is the identification of a novel weight function, wα(x) = x−(2α−1)e−x, which is essential to prove the orthogonality of these functions over the interval [0,∞). Comprehensive numerical validation is provided, confirming the theoretical orthogonality across a wide range of fractional orders α and demonstrating a clean reduction to the classical polynomials when α = 2. An analysis of computational feasibility confirms the practical applicability of these functions for solving fractional differential equations and other applied problems.

Abstract

Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications.This study investigates the suppression of chaos in a three-variable reaction system through an optimal linear feedback strategy, formulated via the solution of an algebraic Riccati equation.The proposed control approach effectively eliminates chaotic oscillations, guiding the system to equilibrium even under parameter uncertainties of up to 20%. Numerical simulations confirm that the control action maintains high robustness, ensuring convergence with minimal effort. The stabilization time for x1 remains close to 29 s across different tolerances, while x2 and x3 converge nearly instantly, demonstrating the rapid effectiveness of the method. Furthermore, the control signal stabilizes at a small positive value after a short transient, reinforcing the computational efficiency and practical feasibility of this approach. These findings demonstrate that optimal linear control techniques provide a reliable and theoretically sound framework for managing nonlinear chemical systems, offering an accessible solution for real-world applications in engineering and process optimization.