Brushless direct current (BLDC) motors are widely used in industrial applications due to their high efficiency and reliability. However, these motors exhibit inherent nonlinear and chaotic behavior, which can degrade performance and cause instability under certain operating conditions. This paper proposes a fractional-order sliding mode controller (FO-SMC) for robust chaos suppression and improved stability in BLDC motor systems to address this issue. The proposed controller leverages fractional-order calculus to enhance robustness, mitigate chattering, and provide better disturbance rejection than conventional control approaches. A comprehensive Lyapunov-based stability analysis is conducted to ensure finite-time convergence and system stability under parameter uncertainties and external disturbances. The effectiveness of the proposed FO-SMC is evaluated through extensive numerical simulations, comparing its performance against the integer-order sliding mode control method. The results demonstrate that FOS-MC significantly outperforms traditional controllers regarding settling time, overshoot reduction, and robustness to external perturbations. Additionally, the study explores the practical feasibility of implementing the proposed control strategy in real-time applications using Grunwald-Letnikov fractional derivatives, which enable efficient numerical approximation and digital implementation in field-programmable gate array-based and microcontroller-driven control systems. The findings confirm that FOS-MC provides a highly adaptive and resilient solution for stabilizing BLDC motors, making it a strong candidate for advanced industrial automation and high-performance motor control applications.

In this work, we utilize infinitesimal symmetries to compute Maxwell points which play a crucial role in studying sub-Riemannian control problems. By examining the infinitesimal symmetries of the geometric control problem on the SH(2) group, particularly through its Lie algebraic structure, we identify invariant quantities and constraints that streamline the Maxwell point computation.

This work introduces a fractional-order model of gambling addiction using the modified Atangana-Baleanu-Caputo operator. We establish solution existence/uniqueness, derive the reproduction number R0, and analyze stability. Numerical results demonstrate how fractional order υ influences addiction dynamics. The model identifies key intervention parameters through sensitivity analysis. The optimal control strategy is proposed to reduce progression to addiction. These approaches provide new tools for understanding and managing problem gambling behaviors.

This study presents an investigation into fractional-order predefined-time terminal sliding mode control (FoPtSMC) for robotic manipulators, particularly focusing on addressing uncertainties and external disturbances. The study introduces a new predefined-time fractional-order SMC method to ensure guaranteed predefined-time convergence and superior tracking performance. This approach also aims to mitigate control input chattering, a common issue in such systems. The Lyapunov analysis is used, and the study establishes the predefined time stability of the proposed closed system. Furthermore, the effectiveness of the proposed FoPtSMC technique is validated through computer simulations applied to a robotic manipulator system.

This paper investigates the implementation of a Fuzzy Model Reference Learning Control (FMRLC) on a Zedboard Zynq-7000 FPGA. The proposed adaptive controller dynamically adjusts its knowledge base and incorporates a memory-based control mechanism to retain and utilize past results in recurring situations. The design and deployment of the controller were carried out using the MATLAB/Simulink environment and applied to the angular position control of a DC motor. Initially, the controller was tested using the FPGA-In-the-Loop (FIL) approach to assess its robustness against disturbances in simulation. Subsequently, it was experimentally validated for real-time motor position control. The results obtained in FIL simulations and experimental tests demonstrate high tracking accuracy and strong disturbance rejection. These findings underscore both the superiority of the proposed controller over the conventional PID controller and the effectiveness of the adopted design methodology.

In this paper, we analyze the numerical aspects of the practical implementation of the generalized active contour model, that has been recently proposed in the literature, for extracting agricultural crop fields with a high level of inhomogeneity from satellite data. We also derive the corresponding Euler-Lagrange equation and discuss its relaxation method.

This study applies the Multi-Step Generalized Differential Transform Method (MSGDTM) and the Jumarie-Stancu Collocation Series Method (JSCSM) to analyze a fractional-order Model (1). The model incorporates Caputo fractional derivatives to capture the nonlocal and memory-dependent characteristics of glucose-insulin interactions, considering physiological factors such as β-cell activity and external glucose intake. Stability analysis reveals bifurcations and chaotic attractors, demonstrating the system’s sensitivity to fractional orders. Numerical simulations compare MSGDTM and JSCSM accuracy and efficiency, highlighting MSGDTM’s superior convergence and lower approximation error. The results show that fractional-order modeling provides a more accurate framework for understanding glucose-insulin dynamics and predicting metabolic behavior. Furthermore, control mechanisms are introduced to mitigate chaos, offering potential strategies for managing diabetes. This work emphasizes the robustness of MSGDTM in solving complex fractional biological models. It provides insights into fractional calculus applications in biomedical research.

The trajectory controllability for fractional order semilinear integrodifferential systems of order ν ∈ (0, 1] and ν ∈ (1, 2] is the subject of this paper. Monotonicity is an important characteristic in many communications applications in which digital-to-analog converter circuits are used. Such applications can function in the presence of nonlinearity, but not in the presence of nonmonotonicity. Therefore, it becomes quite interesting to study a problem assuming the monotonicity of the nonlinear function. With the help of fractional calculus, adequate conditions have been developed to verify the trajectory controllability for fractional order semilinear integrodifferential system using the basics of monotone nonlinearity and coercivity. Finally, some examples are presented to demonstrate the viability of the acquired results.

This paper aims to investigate sufficient criteria of the existence solution for a new category of nonlinear fractional differential equation under the Hilfer fractional derivative. The primary existence results are achieved by using a modified version of the Krasnoselskii-Dhage fixed-point theorem in the weighted Banach space. Finally, an application is illustrated to test the validity of the findings.

Nonlinear phenomena are prevalent in numerous fields, including economics, engineering, and natural sciences. Computational science continues to advance through the development of novel numerical schemes and the refinement of existing ones. Ideally, these numerical systems should offer both high-order convergence and computational efficiency. This article introduces a new three step algorithm for solving nonlinear scalar equations, aiming to meet these criteria. The proposed approach requires six function evaluations per iteration and achieves ninth-order convergence. To demonstrate the efficiency of the technique, various numerical examples are shown. Implementations of the method are available in both Maple and Python, and it can be readily adapted for use in other computational environments.

In modern industrial automation, control of nonlinear systems with complex dynamics poses significant challenges, especially when dealing with discrete time models that incorporate state-dependent parameters. Addressing this need, this paper explores the Proportional-integral-derivative-plus (PID+) control approach applied to nonlinear systems characterized by state-dependent parameter (SDP) discrete-time models. Two industrial applications are demonstrated as follows: a bitumen tank system and a reeling/packing machine used in a bitumen membrane sheet production line. Both systems are modeled using discrete-time transfer functions with SDP structures. The present work extends the novel SDP-PID+ approach by formulating its control algorithms and integrating additional proportional and input compensators. This enhancement enables effective and intuitive handling of processes characterized by discrete-time transfer functions with any order and sampling time delay. The approach enables a straightforward implementation of the SDP-PID+ algorithm across two distinct industrial applications, considering their varying response times. The approach reduces the time required to design the SDP-PID+ method for the selected applications while also demonstrating enhanced robustness and performance. It effectively mitigates disturbances and accommodates nonlinearities, higher-order dynamics, and delays.

This paper introduces a robust distributed-order time-fractional telegraph model, incorporating Caputo time- and Riesz space-fractional derivatives. The spatial Riesz derivative is discretized using an optimized finite difference method. For the distributed-order fractional operator, the midpoint rule was first used to approximate the integral with respect to the order distribution, followed by the application of a finite difference scheme to approximate the Caputo time-fractional derivative. The method’s flexibility and high accuracy make it a valuable tool for modeling and simulating these systems, providing insights into the behavior of fractional-order systems with both temporal and spatial fractional effects. Additionally, the proposed approach outperforms existing numerical methods in terms of both precision and computational efficiency, making it highly applicable for real-world problems requiring accurate and efficient solutions. A comprehensive analysis of convergence and stability was conducted to validate the proposed numerical method. To demonstrate its effectiveness, several numerical simulations were performed, revealing the method’s exceptional accuracy and computational efficiency. Furthermore, a comparison with existing numerical approaches from the literature is provided, highlighting the proposed method’s superior performance in both precision and practical applicability.