Search Results (2,926)

High-water material (HWM) is widely used for roadside filling in gob-side entry retaining (GER), where its creep behavior under sustained loading critically influences the long-term stability of the roadway. To enhance the long-term mechanical performance of HWM, this study modified it with polyethylene (PE) fiber and conducted uniaxial compression creep tests to investigate the effects of fiber content on time-dependent deformation, long-term strength, and failure time. The results indicate that when the applied stress remains below the long-term strength, the creep deformation of PE fiber-modified HWM stabilizes over time. In contrast, under higher stress levels, the deformation of HWM continuously develops over time and progresses through three stages: attenuation, steady-state, and accelerated creep, ultimately resulting in failure. Compared with pure HWM, the fiber-modified material exhibits a significant improvement in long-term strength, which increases linearly with fiber content. Furthermore, a higher fiber content raises the stress threshold for creep failure and substantially extends the time to failure. To predict the creep response of PE fiber-modified HWM, a viscoelastic-plastic creep damage model was developed using the component combination method, incorporating the Riemann–Liouville fractional-order integral operator and a time-dependent damage evolution equation. The reliability of the model was verified by utilizing the experimental data, and a sensitivity analysis of the model parameters was carried out based on the fitting results. The proposed model can not only describe the creep behavior of HWM across all loading stages, including the accelerated creep phase, but also accounts for the effect of fiber content on long-term strength. These findings can provide a theoretical foundation for the design and stability assessment of fiber-reinforced HWM roadside backfills in GER engineering. Full article

In this paper, we investigate the finite-time consensus problem of a fractional-order multi-agent system with repetitive motion. The system under consideration consists of robotic agents with a leader and a fixed communication topology. A distributed open-closed-loop PDα fractional-order iterative learning control (FOILC) algorithm is proposed. The finite-time uniform convergence of the proposed algorithm is analyzed, and sufficient convergence conditions are derived. The theoretical analysis demonstrates that, as the number of iterations increases, each agent can achieve complete tracking within a finite time by appropriately selecting the gain matrices. Simulation results are presented to verify the effectiveness of the proposed method. Full article

In this article, we propose an expanded mixed finite element method for variable-coefficient fractional dispersion equations (FDEs). By introducing two intermediate variables, $p=Du$ and $\sigma =-I_{\theta }^{\beta }p$, the FDEs are reformulated into a mixed system involving only lower-order derivatives. Based on this, we construct an expanded mixed variational framework and prove the weak coercivity in the sense of the LBB condition over appropriately chosen Sobolev spaces, thereby ensuring the well-posedness of the formulation. Then, we develop an expanded mixed finite element scheme and prove that the unique expanded finite element solution possesses optimal approximation accuracy to the fractional flux $\sigma ,$ the gradient p and the unknown u. Finally, numerical experiments are conducted to verify the efficiency and accuracy of the proposed method. Full article

This paper addresses the limitations of conventional single-stage direct-control maximum power point tracking (MPPT) methods, such as the Perturb and Observe (P&O) algorithm. Fixed-step-size duty-cycle perturbations cause a trade-off between slow tracking with small oscillations and fast tracking with large oscillations, along with poor responsiveness to rapid weather variations and output voltage fluctuations. Two main contributions are presented. First, a fractional-order DC–DC boost converter (FOBC) is introduced, incorporating fractional-order dynamics to enhance system performance beyond improvements in control algorithms alone. Second, a novel indirect-control MPPT strategy based on a two-stage architecture is developed, where the P&O algorithm generates the optimal voltage reference and a fractional-order linear-quadratic-integral (FOLQI) controller—designed using a fractional-order small-signal model—regulates the PV module voltage to generate the FOBC duty cycle. Hardware-in-the-loop simulations confirm substantial performance improvements. The proposed FOLQI-based indirect-control approach with FOBC achieves a maximum MPPT efficiency of 99.26%. An alternative indirect method using a classical linear-quadratic-integral (LQI) controller with an integer-order boost converter reaches 98.38%, while the conventional direct-control P&O method achieves only 94.21%, demonstrating the superiority of the proposed fractional-order framework. Full article

This paper presents a reduced-order Legendre–Galerkin extrapolation (ROLGE) method combined with the scalar auxiliary variable (SAV) approach (ROLGE-SAV) to numerically solve the time-fractional Allen–Cahn equation (tFAC). First, the nonlinear term is linearized via the SAV method, and the linearized system derived from this SAV-based linearization is time-discretized using the shifted fractional trapezoidal rule (SFTR), resulting in a semi-discrete unconditionally stable scheme (SFTR-SAV). The scheme is then fully discretized by incorporating Legendre–Galerkin (LG) spatial discretization. To enhance computational efficiency, a proper orthogonal decomposition (POD) basis is constructed from a small set of snapshots of the fully discrete solutions on an initial short time interval. A reduced-order LG extrapolation SFTR-SAV model (ROLGE-SFTR-SAV) is then implemented over a subsequent extended time interval, thereby avoiding redundant computations. Theoretical analysis establishes the stability of the reduced-order scheme and provides its error estimates. Numerical experiments validate the effectiveness of the proposed method and the correctness of the theoretical results. Full article

This study addresses the issue of nonfragile state estimation for fractional-order memristive neural networks with time-varying delays under an adaptive event-triggered mechanism. Possible gain perturbations of the estimator are considered. A Bernoulli-distributed random variable is introduced to model the stochastic nature of gain fluctuations. The primary objective is to develop a nonfragile estimator that accurately estimates the network states. By means of Lyapunov functionals and fractional-order Lyapunov methods, two delay and order-dependent sufficient criteria are established to guarantee the mean-square stability of the augmented system. Finally, the effectiveness of the proposed estimation scheme is demonstrated through two simulation examples. Full article

This paper presents a novel high-order numerical method. The proposed scheme utilizes polynomial generating functions to achieve p order accuracy in time for the Grünwald–Letnikov fractional derivatives, while maintaining second-order spatial accuracy. By incorporating a short-memory principle, the method remains computationally efficient for long-time simulations. The authors rigorously analyze the stability of equilibrium points for the fractional vegetation–water model and perform a weakly nonlinear analysis to derive amplitude equations. Convergence analysis confirms the scheme’s consistency, stability, and convergence. Numerical simulations demonstrate the method’s effectiveness in exploring how different fractional derivative orders influence system dynamics and pattern formation, providing a robust tool for studying complex fractional systems in theoretical ecology. Full article

With the rapid development of Internet of Things (IoT) and Artificial Intelligence (AI) technologies, information security has become a critical issue. To develop a highly secure image encryption transmission system, this study proposes a novel key generation mechanism based on the combination of fractional-order chaotic system synchronization control and the SHA-256 algorithm. This proposed method dynamically generates high-quality synchronous random number sequences and is combined with the Advanced Encryption Standard (AES) algorithm. To quantitatively evaluate the mechanism, the generated sequences are tested using NIST SP 800-22, ENT, and DIEHARD suites. The comparative results show that the key generation mechanism produces sequences with higher randomness and unpredictability. In the evaluation of image encryption, histogram distribution, information entropy, adjacent pixel correlation, NPCR, and UACI are used as performance metrics. Experimental results show that the histogram distributions are uniform, the values of information entropy, NPCR, and UACI are close to their ideal levels, and the pixel correlation is significantly reduced. Compared to recent studies, the proposed method demonstrates higher encryption performance and stronger resistance to statistical attacks. Furthermore, the system effectively addresses key distribution and management problems inherent in traditional symmetric encryption schemes. These results validate the reliability and practical feasibility of the proposed approach. Full article

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift, information loss for real-valued spectral components, and the absence of tunable parameters. The graph fractional Fourier transform introduces domain flexibility through a fractional order parameter $\alpha$ but does not resolve the issues of phase rigidity and information loss. Inspired by the dual-parameter fractional Hilbert transform (FRHT) in classical signal processing, we propose the graph FRHT (GFRHT). The GFRHT incorporates a dual-parameter framework: the fractional order $\alpha$ enables analysis across arbitrary fractional domains, interpolating between vertex and spectral spaces, while the angle parameter $\beta$ provides adjustable phase shifts and a non-zero real-valued response ($cos\beta$) for real eigenvalues, thereby eliminating information loss. We formally define the GFRHT, establish its core properties, and design a method for graph analytic signal construction, enabling precise envelope extraction and demodulation. Experiments on anomaly identification, speech classification and edge detection demonstrate that GFRHT outperforms GHT, offering greater flexibility and superior performance in graph signal processing. Full article

This research work investigates the existence, uniqueness, and stability of solution for a time-fractional fourth-order partial differential equation, subject to two initial conditions and four nonlocal integral boundary conditions. The equation incorporates several key components: the Caputo fractional derivative operator, the Laplace operator, the biharmonic operator, as well as terms representing frictional and viscoelastic damping. The presence of these elements, particularly the nonlocal boundary constraints, introduces new mathematical challenges that require the development of advanced analytical methods. To address these challenges, we construct a functional analytic framework based on Sobolev spaces and employ energy estimates to rigorously prove the well-posedness of the problem. Full article

In order to achieve better accuracy, modern models have become increasingly large, leading to an exponential increase in computational load, making it challenging to apply them to edge computing. Binary neural networks (BNNs) are models that quantize the filter weights and activations to 1-bit. These models are highly suitable for small chips like advanced RISC machines (ARMs), field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), system-on-chips (SoCs) and other edge computing devices. To design a model that is more friendly to edge computing devices, it is crucial to reduce the floating-point operations (FLOPs). Batch normalization (BN) is an essential tool for binary neural networks; however, when convolution layers are quantized to 1-bit, the floating-point computation cost of BN layers becomes significantly high. This paper aims to reduce the floating-point operations by removing the BN layers from the model and introducing the scaled weight standardization convolution (WS-Conv) method to avoid the significant accuracy drop caused by the absence of BN layers, and to enhance the model performance through a series of optimizations, adaptive gradient clipping (AGC) and knowledge distillation (KD). Specifically, our model maintains a competitive computational cost and accuracy, even without BN layers. Furthermore, by incorporating a series of training methods, the model’s accuracy on CIFAR-100 is 0.6% higher than the baseline model, fractional activation BNN (FracBNN), while the total computational load is only 46% of the baseline model. With unchanged binary operations (BOPs), the FLOPs are reduced to nearly zero, making it more suitable for embedded platforms like FPGAs or other edge computers. Full article

Cancer remains a significant challenge in the field of medicine, primarily due to its inherent plasticity and the development of resistance to conventional therapeutic interventions. Genomic mutations and the activation of oncogenes enable cancer cells to resist senescence and apoptosis, leading to uncontrolled growth with harmful consequences. Small peptides are molecules with interesting anti-tumour properties and represent a valid alternative to conventional treatments. Our group has previously identified a class of small peptides bound to the DNA that can be extracted from the chromatin of various tissues, including wheat germ and trout. These peptide pools have been shown to possess interesting antiproliferative and apoptotic properties, and they are associated with cell cycle regulation. However, given the complexity of the extraction process, it is necessary to identify a substrate that will enable a more efficient extraction of these peptides, while also ensuring a composition that is simple to investigate. The present study developed a method for the extraction of this group of peptides from yeast, and the extract was then tested on cancer cells in order to confirm its anti-tumoral properties. The peptides were obtained from chromatin extracted from Saccharomyces cerevisiae cells through alkalisation and purification by gel filtration chromatography. The extract was tested on HeLa cells to verify its effects on vitality and the cell cycle. The data demonstrate that the chromatographic profile of this peptide extract indicates a more basic composition than the pool extracted from other tissues and exhibits comparable antiproliferative properties. The ability to rapidly obtain a biologically active, analytically accessible, and adequately purified fraction from the widely available substrate Saccharomyces cerevisiae represents a significant advance in the study of these DNA-binding peptides. Full article

This study explores finite-time synchronization (FTS) in fractional-order quaternion-valued neural networks (FQVNNs) characterized by discontinuous activation functions and uncertainties in parameters. Initially, leveraging the properties of the Mittag-Leffler function along with fractional-order (F-O) delayed differential inequalities, a novel finite-time stability theorem for F-O systems is established, building upon previous research findings. Next, based on norm definitions, two state feedback controllers employing quaternion 1-norm and quaternion 2-norm are devised to ensure FTS for the system under consideration. Following this, by utilizing differential inclusion theory, examining the quaternion sign function, employing advanced inequality methods, applying principles of F-O differential equations, and using the Lyapunov functional approach, new criteria for achieving FTS in FQVNNs are formulated. Additionally, precise estimates for the settling time are presented. In conclusion, two carefully designed numerical examples are included to corroborate the theoretical results derived. Full article

In the current study, we used Chebyshev’s Pseudospectral Method (CPM), a novel numerical technique, to solve nonlinear third-order Emden–Fowler delay differential (EF-DD) equations numerically. Fractional derivatives are defined by the Caputo operator. These kinds of equations are transformed to the linear or nonlinear algebraic equations by the proposed approach. The numerical outcomes demonstrate the precision and efficiency of the suggested approach. The error analysis shows that the current method is more accurate than any other numerical method currently available. The computational analysis fully confirms the compatibility of the suggested strategy, as demonstrated by a few numerical examples. We present the outcome of the offered method in tables form, which confirms the appropriateness at each point. Additionally, the outcomes of the offered method at various non-integer orders are investigated, demonstrating that the result approaches closer to the accurate solution as a value approaches from non-integer order to an integer order. Additionally, the current study proves some helpful theorems about the convergence and error analysis related to the aforementioned technique. A suggested algorithm can effectively be used to solve other physical issues. Full article

Economic dispatch in wind-integrated power systems is a critical challenge, yet many recent metaheuristics suffer from premature convergence, heavy parameter tuning, and limited ability to escape local optima in non-smooth valve-point landscapes. This study proposes a new hybrid optimization framework, the Fractional Grasshopper Optimization algorithm (FGOA), which integrates fractional-order calculus into the standard Grasshopper Optimization algorithm (GOA) to enhance its search efficiency. The FGOA method is applied to the economic load dispatch (ELD) problem, a nonlinear and nonconvex task that aims to minimize fuel and wind-generation costs while satisfying practical constraints such as valve-point loading effects (VPLEs), generator operating limits, and the stochastic behavior of renewable energy sources. Owing to the increasing role of wind energy, stochastic wind power is modeled through the incomplete gamma function (IGF). To further improve computational accuracy, FGOA is hybridized with Sequential Quadratic Programming (SQP), where FGOA provides global exploration and SQP performs local refinement. The proposed FGOA-SQP approach is validated on systems with 3, 13, and 40 generating units, including mixed thermal and wind sources. Comparative evaluations against recent metaheuristic algorithms demonstrate that FGOA-SQP achieves more accurate and reliable dispatch outcomes. Specifically, the proposed approach achieves fuel cost reductions ranging from 0.047% to 0.71% for the 3-unit system, 0.31% to 27.25% for the 13-unit system, and 0.69% to 12.55% for the 40-unit system when compared with state-of-the-art methods. Statistical results, particularly minimum fitness values, further confirm the superior performance of the FGOA-SQP framework in addressing the ELD problem under wind power uncertainty. Full article