Search Results (125)

Asymmetric functional-order (variable-order) fractional diffusion–wave equations (FO-FDWEs) introduce considerable computational challenges, as the fractional order of the derivatives can vary spatially or temporally. To overcome these challenges, a novel spectral method employing generalized fractional-order Chelyshkov wavelets (FO-CWs) is developed to efficiently solve such equations. In this approach, the Riemann–Liouville fractional integral operator of variable order is evaluated in closed form via a regularized incomplete Beta function, enabling the transformation of the governing equation into a system of algebraic equations. This wavelet-based spectral scheme attains extremely high accuracy, yielding significantly lower errors than existing numerical techniques. In particular, numerical results show that the proposed method achieves notably improved accuracy compared to existing methods under the same number of basis functions. Its strong convergence properties allow high precision to be achieved with relatively few wavelet basis functions, leading to efficient computations. The method’s accuracy and efficiency are demonstrated on several practical diffusion–wave examples, indicating its suitability for real-world applications. Furthermore, it readily applies to a wide class of fractional partial differential equations (FPDEs) with spatially or temporally varying order, demonstrating versatility for diverse applications. Full article

This study investigates the influence of rotation on wave propagation in a semiconducting nanostructure thermoelastic solid subjected to a ramp-type heat source within a two-temperature model. The thermoelastic interactions are modeled using the two-temperature theory, which distinguishes between conductive and thermodynamic temperatures, providing a more accurate description of thermal and mechanical responses in semiconductor materials. The effects of rotation, ramp-type heating, and semiconductor properties on elastic wave propagation are analyzed theoretically. Governing equations are formulated and solved analytically, with numerical simulations illustrating the variations in thermal and elastic wave behavior. The key findings highlight the significant impact of rotation, nonlocal parameters $e_{0}a$, and time derivative fractional order (FO) $\alpha$ on physical quantities, offering insights into the thermoelastic performance of semiconductor nanostructures under dynamic thermal loads. A comparison is made with the previous results to show the impact of the external parameters on the propagation phenomenon. The numerical results show that increasing the rotation rate $\mathsf{\Omega }=5$ causes a phase lag of approximately 22% in thermal and elastic wave peaks. When the thermoelectric coupling parameter ${\mathsf{\epsilon }}_3$ is increased from $-0.8\times {10}^{-42}$ to $1.2\times {10}^{-42}$. The temperature amplitude rises by 17%, while the carrier density peak increases by over 25%. For nonlocal parameter values $\mathsf{\epsilon }=0.3\to 0.6$, high-frequency stress oscillations are damped by more than 35%. The results contribute to the understanding of wave propagation in advanced semiconductor materials, with potential applications in microelectronics, optoelectronics, and nanoscale thermal management. Full article

The time-dependent creep behavior of coal is essential for assessing long-term structural stability and operational safety in deep coal mining. Therefore, this work develops a full-stage creep constitutive model. By integrating fractional calculus theory with statistical damage mechanics, a nonlinear fractional-order (FO) damage creep model is constructed through serial connection of elastic, viscous, viscoelastic, and viscoelastic–plastic components. Based on this model, both one-dimensional and three-dimensional (3D) fractional creep damage constitutive equations are acquired. Model parameters are identified using experimental data from deep coal samples in the mining area. The result curves of the improved model coincide with experimental data points, accurately describing the deceleration creep stage (DCS), steady-state creep stage (SCS), and accelerated creep stage (ACS). Furthermore, a sensitivity analysis elucidates the impact of model parameters on coal creep behavior, thereby confirming the model’s robustness and applicability. Consequently, the proposed model offers a solid theoretical basis for evaluating the sustained stability of deep coal mining and has great application potential in deep underground engineering. Full article

Cardiac pacemakers are standard implantable medical devices that regulate and treat heart rhythm disorders, primarily aiming to improve patient health outcomes. This study presents the systematic design, implementation, and simulation-based validation of a novel fuzzy-immune adaptive Fractional-Order Linear Quadratic Integral (FO-LQI) control strategy for heart rate (HR) regulation using cardiac pacemakers. Unlike the conventional LQI controller, the proposed approach replaces the integer-order integrator with a fractional-order integral operator to enhance the controller’s design flexibility and dynamic response. To address the implementation challenges of fixed fractional exponents, a fuzzy-immune adaptation mechanism is introduced to modulate the fractional order in real time. This adaptive scheme improves the controller’s robustness across varying physiological states, enabling more responsive HR adaptation to the patient’s metabolic demands. The proposed controller is modeled and simulated in MATLAB/Simulink using physiologically relevant test cases. Comparative simulation results show that the fuzzy-immune adaptive FO-LQI controller outperforms the baseline LQI and fixed FO-LQI controllers in achieving time-optimal HR regulation. These findings validate the reliability and enhanced robustness of the proposed control scheme for simulating cardiac behavior under diverse physiological conditions. Full article

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses. Full article

The present work proposes a novel fractional-order multifunction filter topology in current-mode (CM), which is designed based on the Modified Current Feedback Operational Amplifier (MCFOA). The proposed design simultaneously generates fractional-order low-pass (FO-LPF), high-pass (FO-HPF), and band-pass (FO-BPF) outputs while utilizing an optimized set of essential active and passive elements, thereby ensuring simplicity, cost efficiency, and compatibility with integrated circuits (ICs). The fractional-order feature allows precise control over the transition slope between the passband and the stopband, enhancing design flexibility. PSpice simulations validated the filter’s theoretical performance, confirming a 1 kHz cut-off frequency, making it suitable for VLF applications such as military communication and submarine navigation. Monte Carlo analyses demonstrate robustness against parameter variations, while a low THD, a wide dynamic range, and low power consumption highlight its efficiency for high-precision, low-power applications. This work offers a practical and adaptable approach to fractional-order circuit design, with significant potential in communication, control, and biomedical systems. Full article

This paper introduces a novel fractional-order fuzzy logic controller (FOFLC) designed for stator voltage control in standalone doubly fed induction generator (DFIG) systems used in wind energy applications. Unlike traditional fuzzy logic controllers (FLCs), which are limited by integer-order dynamics, the FOFLC leverages the advanced principles of fractional-order (FO) calculus. By integrating fuzzy logic with fractional-order operators, the FOFLC enhances system precision, adaptability, and interpretability while addressing the inherent limitations of conventional proportional-integral (PI) controllers and integer-order FLCs. A key innovation of the FOFLC is its dual-mode architecture, enabling it to operate seamlessly as either a traditional FLC or a fractional-order FOFLC controller. This versatility allows for independent tuning of fractional parameters, optimizing the system’s response to transients, steady-state errors, and disturbances. The controller’s flexibility makes it particularly well-suited for nonlinear and dynamically complex stand-alone renewable energy systems. The FOFLC is experimentally validated on a 3-kW DFIG test bench using the dSPACE-1104 platform under various operating conditions. Compared to a conventional PI controller, the FOFLC demonstrated superior performance, achieving 80% reduction in response time, eliminating voltage overshoot and undershoot, reducing stator power and torque ripples by over 46%, and decreasing total harmonic distortion (THD) of both stator voltage and current by more than 50%. These results confirm the FOFLC’s potential as a robust and adaptive control solution for stand-alone renewable energy systems, ensuring high-quality power output and reliable operation. Full article

Chaotic behavior and memory-dependent dynamics in fractional-order brushless DC motors (FOBLDCMs) pose significant challenges for robust and stable control design, particularly when physical constraints such as actuator saturation and rate limitations are present. Existing control frameworks often neglect these nonlinear limitations, resulting in performance degradation and potential instability in practical applications. Motivated by these challenges, this paper presents a comprehensive Lyapunov-based stability and control synthesis framework for FOBLDCMs within the fractional-order (FO) range $0<v<1$. The proposed methodology employs indirect, direct, and composite Lyapunov functions to derive sufficient stability conditions under four scenarios: unconstrained input, saturation-only, rate-limited-only, and combined constraints. For each case, a family of stabilizing controllers is designed to explicitly handle the respective limitations. To the best of our knowledge, this is the first study to rigorously address both saturation and rate limitations in the control design of FO chaotic systems. Numerical simulations confirm that the proposed controllers significantly improve performance over existing methods. Specifically, the unconstrained controller achieves a notable reduction in control energy (from $2.72\times {10}^5$ to $1.83\times {10}^5$), a 26.3% decrease in maximum control effort, and enhanced or comparable tracking accuracy, as indicated by lower ISE and RMSE values. These results highlight the robustness and practical applicability of the proposed control framework for real-world FO electromechanical systems. Full article

This paper explores the problems of slow response speed, poor anti-interference performance, and low control accuracy that exist in traditional Active Disturbance Rejection Control methods in Buck-type DC/DC converters. To address these issues, a fractional-order Active Disturbance Rejection Control (FO-LADRC) controller is proposed to enhance the dynamic characteristics and anti-interference ability of Buck-type DC/DC converters, while expanding the control range and flexibility of traditional linear Active Disturbance Rejection Control (LADRC). Firstly, the mathematical model of the Buck-type DC/DC converter is established. Secondly, based on Active Disturbance Rejection Control, a fractional-order linear Extended State Observer (FO-LESO) is constructed to estimate the model error and external disturbance of the system. Then, the stability of the system is studied through transfer function and error analysis. Finally, the effectiveness of the FO-LADRC controller method is verified through simulation. The simulation and experiment results show that the proposed FO-LADRC method outperforms traditional PI and LADRC methods in terms of dynamic performance. It can effectively improve the dynamic characteristics of the system and enhance the anti-interference ability of the system. Full article

This paper presents a new method for the simultaneous estimation of system states and unknown inputs in fractional-order Takagi–Sugeno (FO-TS) systems with unmeasurable premise variables (UPVs), by introducing a fractional-order proportional-integral unknown input observer (FO-PIUIO) based on partial state augmentation. This approach permits the estimation of both states and unknown inputs, which are essential for system monitoring and control. Partial state augmentation allows the integration of unknown inputs into a partially augmented model, ensuring accurate estimates of both states and unknown inputs. The state estimation error is formulated as a perturbed system. The convergence conditions for the state estimation errors between the system and the observer are derived using the second Lyapunov method and the $L_2$ approach. Compared to traditional integer-order unknown input observers or fuzzy observers with measurable premise variables, in our method, fractional-order dynamics are combined with partial state augmentation uniquely for the persistent estimation of states along with unknown inputs in unmeasurable premise variable systems. Such a combination allows for robust estimation even under uncertainties in systems and long memory phenomena and is a significant step forward from traditional methods. Finally, a numerical example is provided to illustrate the performance of the proposed observer. Full article

To address the critical challenge of controlling tiltrotor aircraft during transition mode, this paper proposes a fractional-order model reference adaptive control (FO-MRAC) method based on the unique modeling of the tiltrotor aircraft. A nonlinear model capturing the dynamic characteristics of the tiltrotor aircraft during the transition mode is developed based on an accurate analysis of the forces and moments acting on key components. This model is subsequently linearized to obtain a stable flight envelope. Considering the complexity of transition, the FO-MRAC method is designed based on the shift of the equilibrium point for superior parameter tuning and disturbance rejection. Then, the stability of the closed-loop system is analyzed using the Lyapunov stability theory. Finally, an experimental platform is constructed to verify the validity of the aerodynamic modeling and the designed control method. Full article

This article investigates non-fragile synchronization control and circuit implementation for incommensurate fractional-order (IFO) chaotic neural networks with parameter uncertainties. In this paper, we explore three aspects of the research challenges, i.e., theoretical limitations of uncertain IFO systems, the fragility of the synchronization controller, and the lack of circuit implementation. First, we establish an IFO chaotic neural network model incorporating parametric uncertainties, extending beyond conventional commensurate-order architectures. Second, a novel, non-fragile state-error feedback controller is designed. Through the formulation of FO Lyapunov functions and the application of inequality scaling techniques, sufficient conditions for asymptotic synchronization of master–slave systems are rigorously derived via the multi-order fractional comparison principle. Third, an analog circuit implementation scheme utilizing FO impedance units is developed to experimentally validate synchronization efficacy and accurately replicate the system’s dynamic behavior. Numerical simulations and circuit experiments substantiate the theoretical findings, demonstrating both robustness against parameter perturbations and the feasibility of circuit realization. Full article

This paper focuses on the application of fractional calculus techniques in the identification and control of multivariable (multiple input—multiple output) systems (MIMO). By considering a previously reported experimental set-up similar to a greenhouse, this study proposes the open-loop identification of fractional order transfer functions relating to the controlled and manipulated variables, which were validated by experimental data. Afterward, the theoretical analysis of Fractional-order Proportional and Integral (FOPI) closed-loop control for this MIMO system was carried out. An important aspect concerns the use of Particle Swarm Optimization (PSO) metaheuristic algorithm for optimization tasks, both in parameter estimation and controller tuning. Moreover, comparisons with integer order models and controllers (IOPID-IMC) were performed. The results demonstrate the superior performance and robustness of the FOPI-PSO fractional control, which achieves up to 79.6% reduction in ITAE and 72.1% reduction in ITSE criteria. Without the need for explicit decouplers, the decentralized FOPI-PSO control structure demonstrated effective handling of interactions between the temperature and humidity control loops, simplifying the control design while maintaining performance. The fractional-order controllers exhibited robustness to measurement noise, as evidenced by stable and precise control responses in the presence of experimental uncertainties. Additionally, the optimized tuning of FOPI controllers implicitly compensated for disturbances and setpoint changes without requiring additional feedforward mechanisms. This study contributes to a better understanding of fractional calculus applications in designing FO–MIMO systems and provides a practical framework for addressing the identified gaps in the field. Full article

This work presents a fractional order Proportional Integral and Derivative controller with adaptation characteristics in the control parameters depending on the required output, gain scheduling fractional order PID (GS-FO-PID). The fractional order PID is applied to the voltage control of a DC–DC buck quadratic converter (QBC). The DC–DC buck quadratic converter is designed to operate at 12 V, although in the simulation tests, the output voltage ranges from 5 to 36 V. The performance of the GS-FO-PID is compared with the one from a classic PID. The GS-FO-PID presents better performance when the reference voltage is changed. In the same way, the behavior of the converter with the reference fixed to 12 V output is analyzed with load changes; for this case, the amplitude value of the ripple when the converter is driven by the GS-FO-PID almost has no variation. Full article

The nonlinear dynamic characteristics of a peak current regulation fractional-order (FO) flyback converter, considering the fractional nature of inductance and capacitance, are investigated in detail. First, the discrete iterative model of the fractional-order (FO) flyback converter under 10 kHz operating conditions is accomplished using the application of the Generalized Euler Method (GEM). On this basis, bifurcation diagrams, phase diagrams, and simulated time domain diagrams are used to describe the nonlinear dynamic behavior of the converter. The nonlinear dynamics of the converter are investigated through bifurcation and phase diagram analyses. A comprehensive examination is conducted to evaluate the impact of key parameters, including input voltage, reference current, and the fractional orders of inductance and capacitance, on the system’s stability. Furthermore, a comparative analysis is performed with conventional integer-order (IO) flyback converters to highlight the distinctive characteristics. The findings demonstrate that the FO converter manifests distinct nonlinear characteristics, including period-doubling bifurcation and chaotic behavior. Moreover, for identical parameter sets, the FO flyback converter is found to possess a smaller stability domain but a larger parameter region for bifurcation and chaos compared to its IO counterpart. This behavior allows the FO converter to more accurately capture the nonlinear dynamic characteristics of the flyback converter. Simulation results further substantiate the theoretical predictions. Full article