Search Results (3,109)

In this paper, we investigate the application of the relative entropy framework for safety assessments of steel elements with structural defects at the micro- and macro-scales. Mathematical theories developed by Bhattacharyya and by Kullback and Leibler (K-L) have been used for this purpose. This approach uses both expectations and variations, similar to the First-Order Reliability Method (FORM), but is extended to include 3rd- and 4th-order central probabilistic moments. It is necessary to use a hybrid computational technique that combines the Finite Element Method (FEM) software ABAQUS CAE 2017 with the implemented Gurson–Tvergaard–Needleman (GTN) damage model and the computer algebra system MAPLE. The iterative generalized stochastic perturbation technique has been used to determine the probabilistic moments of structural response, to utilize the Weighted Least Squares Method to approximate the structural response function, and to determine uncertainty in the stress, strain, and displacement state functions. This approach is based on relative entropy because of its universality. There is no need to assume a type of distribution of the state functions, in contrast to FORM, where a Gaussian distribution is required. This paper verifies whether relative entropy can serve as an alternative to FORM for determining reliability. The yield surface of the porous material with a random values of the void volume fraction f are also presented. Full article

This study addresses the need for applied sentiment analysis in engineering decision-support systems by presenting a hybrid framework for domain-specific engineering text. This study presents a hybrid sentiment classification framework by integrating transformer-based semantic embeddings with fractional-order feature modeling. The proposed BERTLR framework combines BERT and RoBERTa representations with Grünwald–Letnikov fractional derivative–enhanced TF-IDF features and logistic regression within a unified soft-voting architecture. Unlike conventional ensemble sentiment models that merely aggregate embeddings and handcrafted features, the proposed method introduces fractional-order feature transformation to capture non-local dependency patterns and memory-aware lexical variations that are often overlooked in technical review text. This design provides a structured fusion of contextual semantic information and fractional statistical representations, supported by SHAP-based explainability and ablation analysis. Experiments conducted on six real-world engineering application domains show consistent improvements over conventional TF-IDF models, LSTM baselines, and non-fractional transformer variants. The framework achieves up to 91% accuracy, together with strong precision, recall, and F1-score performance. These results demonstrate that fractional-order feature augmentation can provide a meaningful complementary signal to transformer embeddings, offering an interpretable and effective sentiment analysis solution for engineering and industrial decision-support applications. Full article

We construct and analyze a family of support-defined Brauer-type configurations canonically associated with the Boolean geometry underlying the Grassmann algebra. The construction is governed by an x-support map on monomial labels, which identifies the vertex set with the Boolean lattice $\mathcal{P}\left(\right[n\left]\right)$. This identification yields a Boolean support quiver isomorphic to the directed Hasse diagram of $\mathcal{P}\left(\right[n\left]\right)$, equivalently, to an oriented hypercube. We then equip the family with a canonical cyclic ordering at each vertex and obtain a genuine connected reduced Brauer configuration in the standard sense, together with its associated Brauer configuration algebra and its standard Brauer quiver. A ghost-variable mechanism is introduced to obtain a connected realization without altering any support-controlled invariants. We prove that polygon membership, valencies, multiplicities, Boolean stratification, and the support quiver are invariant under support-preserving ghost relabelings. We also give an explicit description of the standard Brauer quiver and show that it is different from the Boolean support quiver. On the algebraic side, we derive closed formulas for the center dimension, the algebra dimension, and the normalization constant of the induced weighted distribution. On the probabilistic side, we distinguish the vertex entropy from the layer entropy, establish an exact decomposition of the former by Hamming layers, and show that the layer distribution is asymptotically concentrated on the middle layers, while extremal vertices and any fixed maximal path contribute a negligible fraction of the total weight. As a consequence, the layer entropy satisfies a logarithmic asymptotic law. We also investigate geometric consequences of the Boolean model transported through the support identification. Coordinate projections produce a rigidity phenomenon for antipodal pairs, providing a combinatorial analogue of Greenberger–Horne–Zeilinger (GHZ)-type fragility, whereas the first Boolean layer exhibits a persistence property analogous to W-type robustness. Together, these results exhibit a concrete bridge between Grassmann combinatorics, Brauer configuration theory, hypercube geometry, and entropy asymptotics. Full article

This study presents a combined numerical and experimental investigation of transient multiphase compressible flow inside a profiled-rotor rotary volumetric compressor. While most existing studies rely on high-fidelity CFD approaches, a low-order thermodynamic chamber-based model implemented in MATLAB Release 2023a is proposed to predict the temporal evolution of pressure, temperature, and vapor volume fraction during the compression cycle. The model is based on mass and energy conservation applied to variable-volume control chambers and incorporates a simplified cavitation criterion derived from local pressure relative to saturation vapor pressure. An open-loop experimental test bench was developed to measure air mass flow rate, suction and discharge pressures, temperatures, torque, and shaft power under controlled operating conditions. These measurements are used to validate the numerical predictions. The results show good agreement between measured and simulated pressure levels and global performance indicators, with deviations quantified using mean absolute percentage error values remaining below 5% over the investigated operating range. The numerical analysis further reveals the occurrence of localized low-pressure zones during the suction phase, indicating incipient cavitation or microbubble formation at specific rotor positions. The proposed modeling approach provides a computationally efficient alternative to full CFD simulations and enables rapid parametric analysis of rotor geometry and operating conditions. The cavitation formulation does not aim to resolve detailed bubble dynamics or erosion mechanisms, but rather to identify cavitation tendency based on thermodynamic pressure thresholds. Full article

Financial time series in turbulent markets exhibit complex long-memory dynamics and multifractal features that traditional deep learning models fail to capture due to inherent exponential forgetting mechanisms. To address this, we propose Frac-Attn-GL, a novel Fractional-order Spatiotemporal Attention-based GRU-LSTM framework. Grounded in the Fractal Market Hypothesis, the model embeds Grünwald–Letnikov fractional-order operators into a dual-channel architecture (FracLSTM and FracGRU) to characterize long-range memory with rigorous power-law decay priors. Furthermore, an extreme-aware asymmetric loss function is designed to drive a dynamic spatiotemporal routing mechanism, enabling adaptive shifts between long-term macro trends and short-term micro shocks. Empirical tests on major U.S. stock indices reveal three significant findings. First, the Frac-Attn-GL framework substantially reduces prediction errors, achieving up to a 93.1% RMSE reduction on the highly volatile NASDAQ index compared to standard baselines. Second, the adaptively learned fractional-order parameters exhibit a consistent quantitative alignment with the market’s empirical multifractal singularity spectrum, supporting the physical interpretability of the model’s endogenous memory mechanism. Finally, hybrid residual multifractal diagnostics indicate that the framework effectively captures deep long-range correlations, reducing the Hurst exponent of the prediction residuals from ~0.83 to approximately 0.50, a level consistent with the absence of significant long-range dependence. Full article

This study develops an extension of the classical Rayleigh–Schrödinger method for solving fractional-order differential equations. The primary objective is to derive the eigenvalues of a Begley–Torvik-type equation. The proposed analytical expression for the eigenvalues, obtained through this methodological advancement, shows excellent agreement with their exact values. This result is obtained by developing the Rayleigh–Schrödinger method and can be used for a wide range of applied problems. As an illustrative example, the Begley–Torvik type equation is used to describe the deformation-strength characteristics of polymer concrete and other modern granular road materials. It should be noted, however, that this represents just one of many potential applications for such fractional-order models. Full article

Metanil Yellow (MY), a highly toxic azo dye used in food products, was removed from aqueous solution using a metal- and halide-free ordered mesoporous carbon (OMC) adsorbent. MY exhibited a strong affinity towards OMC in batch as well as column operations, and OMC performed much better than previously reported adsorbents. The pH, dye concentration, adsorbent dosage, and contact time were optimised, and detailed adsorption experiments were performed under these conditions. Several isotherm models were fitted to the adsorption data, showing that the Langmuir and the Freundlich adsorption models were followed. Adsorption was spontaneous and endothermic at all measurement temperatures. On the basis of pH studies, enthalpy data, and adsorption isotherm analysis, adsorption was determined to be by physisorption. In kinetics studies, the adsorption process was found to be pseudo-second order with interparticle diffusion as the rate-limiting step. Column experiments using a fixed bed of OMC resulted in almost 100% column efficiency and a fractional column capacity of 0.999. During adsorption/desorption cycles of the exhausted column, 99.71% of the dye was recovered after the first cycle and 97.66% after the eleventh. These findings indicate that OMC is a promising and efficient material for the adsorptive removal of toxic MY dye. Full article

This article proposes a novel approach for dealing with the time-fractional Navier–Stokes equations via the natural generalized Laplace transform decomposition method (NGLTDM). This hybrid method utilizes both the natural generalized Laplace transform (NGLT) and a decomposition method. The method is correct because the series solutions become more accurate when more terms are added. We establish precise theorems that verify the existence of solutions and the convergence of the series. The analysis shows that the suggested method is more general than the Homotopy Perturbation Method (HPM) and the Adomian Decomposition Method (ADM). Also, this approach can be applied to handle difficult fluid dynamics problems governed by the Navier–Stokes equations. This study enhances analytical methodologies for fractional-order flow models. Full article

This study models trachoma transmission in Cameroon using a deterministic approach with integer and fractional-order derivatives, incorporating direct, fly-mediated, and environmental transmission routes. Fitting disease data from 1990–2019, the model forecasts trachoma prevalence until 2035. The research confirms the solution existence and uniqueness, calculates the basic reproduction number ${\mathcal{R}}_0^{\lambda }$ where $\lambda \in (0,1]$ represents the fractional-order parameter, and analyzes equilibrium stability. A stable trachoma-free equilibrium exists when ${\mathcal{R}}_0^{\lambda }<1$, while an endemic equilibrium is proven stable for ${\mathcal{R}}_0^{\lambda }>1$ under specific conditions. Calibration of a fractional model with Cameroon data yielded an ${\mathcal{R}}_0$ of 1.169 (indicating endemicity) and identified an optimal fractional order of $\lambda =0.98$. By calculating the strength number, we found that another epidemic wave could occur in 50 years. Global sensitivity analysis highlighted key parameters affecting trachoma dynamics. A numerical scheme of the model based on the Adams–Bashforth–Moulton method is constructed and its stability demonstrated. It is then used to perform several numerical simulations, first to validate the theoretical results obtained, and then to compare the different models (statistical and deterministic). The conclusion is reached that the disease will persist in the population (${\mathcal{R}}_0>1$), although the statistical model shows that it could disappear by 2030. This proves that, for trachoma dynamics in Cameroon, it is advisable to use a deterministic model. Full article

This paper studies a novel nonlinear fractional-order financial stress model involving Atangana–Baleanu–Caputo (ABC) operators. It focuses on memory effects that are both constant and variable. The novelty of the proposed framework lies in combining multiple interconnected channels of systemic stress into one fractional dynamical model and looks at how they change over time and how they respond to sustained external perturbations. Theoretically, we prove well-posedness results and study the equilibrium structure and stability of the given model. On the computational side, we use numerical simulations of the individual stress components and an aggregate systemic stress index to look into short-term dynamics under different memory regimes. We also include a shock-response analysis to show how memory effects change the way stress builds up, relaxes, and spreads when forced. The sensitivity analysis shows that systemic stress is amplified by the forcing and interaction parameters and reduced by the damping parameters. These findings demonstrate that the model provides a new and effective tool for studying systemic financial instability in a fractional setting. Full article

Accurate and trustworthy prediction of lithium-ion battery aging remains challenging due to multi-mechanistic degradation, cell-to-cell variability, and distribution shift between laboratory calibration and deployment. Fractional-order models have been proposed to capture long-memory effects in electrochemical systems; however, it remains unclear when such memory is empirically identifiable and beneficial within the common prognostics abstraction of state-of-health (SOH) versus cycle index. This work develops a fully reproducible computational pipeline for mechanistic battery aging based on a Caputo fractional differential equation (FDE) and evaluates its cross-cell generalization on open NASA cycling data. Parameters are identified using bounded robust nonlinear least squares and validated under a strict transfer protocol: calibration on cells B0005/B0006 and evaluation on held-out cells B0007/B0018 without refitting. The fractional model is benchmarked against a classical ODE surrogate, an ECM-inspired resistance-proxy baseline, and one-step-ahead machine-learning predictors. Uncertainty quantification is performed via parameter bootstrap and subsequently calibrated using conformal correction to target nominal coverage under transfer. Results show that the fractional order tends to collapse toward the integer-order limit (α → 1) in this dataset, indicating limited evidence of additional long-memory at the SOH-versus-cycle level under the considered protocol, while robust identification remains essential for stability. Calibrated prediction intervals achieve near-nominal coverage on held-out cells, highlighting the importance of UQ calibration under cell-to-cell shift. The proposed scripts and environment specifications enable direct replication and facilitate future extensions to stress-aware fractional models and hybrid physics–ML approaches. Full article

We propose a dimensionally consistent fractional spatio-temporal PDE framework for modelling immune-mediated demyelination in multiple sclerosis (MS). The system couples effector and regulatory T cells, M1/M2 macrophage polarisation, pro- and anti-inflammatory cytokines, oligodendrocyte dynamics, and time-dependent therapeutic controls within a unified distributed-parameter structure. In contrast to ad hoc replacements of integerorder derivatives by Caputo fractional derivatives, the fractional extension proposed here is derived from an underlying continuous-time random walk (CTRW) process with Mittag–Leffler-distributed residence times. This stochastic derivation yields a governing system in which a single commensurate fractional order α ∈ (0, 1], together with a characteristic memory timescale τ0, ensures dimensional consistency and mass balance across all coupled components. The model is formulated as a system of nonlinear reaction–diffusion equations with cross-regulatory and multiplicative interaction terms governing immune amplification, cytokine feedback, and the demyelination–remyelination balance. Analytical interpretation shows how non-Markovian residence times induce Mittag–Leffler-type relaxation and thereby modify effective growth, decay, and stability properties. Numerical simulations compare classical and fractional dynamics, revealing that memory-driven kinetics prolong effector T-cell and M1-macrophage activity, attenuate reparative M2 and oligodendrocyte responses, and extend the effective action of bang–bang therapy inputs representing IFN-β and glatiramer acetate beyond their dosing windows. The results indicate that integer-order models may underestimate chronic inflammatory persistence and demyelination severity, while providing a mathematically and physically well-posed platform for memory-aware immune modelling and therapy evaluation in MS. Full article

Quadrotor UAVs present a significant control challenge due to their underactuated nature; strong coupling effects; nonlinear dynamics; and high sensitivity to unknown effect parameters, external disturbances, and uncertainties. To address this issue, this study proposes a Lyapunov-based backstepping (LYP) controller that ensures robust stability and precise trajectory tracking. The controller employs an inner- and outer-loop architecture for coupled position and attitude control. Its performance is compared with Proportional–Integral–Derivative (PID) and Fractional-Order PID (FOPID) controllers under three scenarios: nominal conditions, external disturbances, and model parameter uncertainties. All controller gains are optimized using Particle Swarm Optimization (PSO). Simulation results, which are evaluated using time-domain metrics and root mean square error (RMSE), demonstrate that the proposed LYP controller achieves superior robustness, faster disturbance rejection, and improved tracking accuracy compared to both PID and FOPID controllers. Full article

This paper presents a unified analytical and computational framework for the study of typhoid fever transmission dynamics governed by a Caputo fractional-order compartmental model of order $\kappa \in (0,1]$. The population is stratified into five epidemiological classes, namely susceptible $\left(\mathcal{S}\right)$, asymptomatic $\left(\mathcal{A}\right)$, symptomatic $\left(\mathcal{I}\right)$, hospitalised $\left(\mathcal{H}\right)$, and recovered $\left(\mathcal{R}\right)$, and the governing system explicitly incorporates asymptomatic transmission, treatment dynamics, and temporary immunity with waning. The use of the Caputo fractional derivative is motivated by the well-documented existence of chronic asymptomatic Salmonella Typhi carriers, whose heavy-tailed sojourn times in the carrier state are naturally encoded by the Mittag–Leffler waiting-time distribution arising from the fractional operator. A complete qualitative analysis of the fractional system is carried out: the basic reproduction number ${\mathcal{R}}_0$ is derived via the next-generation matrix method; local and global asymptotic stability of both the disease-free equilibrium ${\mathcal{E}}_0$ (when ${\mathcal{R}}_0\le 1$) and the endemic equilibrium ${\mathcal{E}}^{*}$ (when ${\mathcal{R}}_0>1$) are established using fractional Lyapunov theory and the LaSalle invariance principle; and the normalised sensitivity indices of ${\mathcal{R}}_0$ are computed to identify transmission-amplifying and transmission-suppressing parameters. Existence, uniqueness, and Ulam–Hyers stability of solutions are established via Banach and Leray–Schauder fixed-point arguments. To complement the analytical results, a fractional physics-informed neural network ($\mathcal{PINN}$) framework is developed to simultaneously reconstruct compartmental trajectories and identify unknown biological parameters from sparse synthetic observations. $\mathcal{PINN}$ embeds the L1-Caputo discretisation directly into the training residuals and employs a four-stage Adam–L-BFGS optimisation strategy to recover five trainable parameters $\mathbf{\Theta }$ = $\{\varphi ,\mu ,\sigma ,\psi ,\beta \}$ across three fractional orders $\kappa \in \{1.0,0.95,0.9\}$. The estimated parameters show strong agreement with the true values at the classical limit $\kappa =1.0$ ($\mathrm{MAPE}=2.27\%$), with the natural mortality rate $\mu$ recovered with $\mathrm{APE}\le 0.51\%$ and the transmission rate $\beta$ with $\mathrm{APE}\le 3.63\%$ across all fractional orders, confirming the structural identifiability of the model. Pairwise correlation analysis of the learned parameters establishes the absence of equifinality, validating that $\beta$ can be reliably included in the trainable set. Noise robustness experiments under Gaussian perturbations of $1\%$, $3\%$, and $5\%$ demonstrate graceful degradation ($\mathrm{MAPE}$: $0.82\%\to 3.10\%\to 7.31\%$), confirming the reliability of the proposed framework under realistic observational conditions. Full article

The development of More Electric Aircraft (MEA) necessitates that Electro-Hydrostatic Actuator (EHA) controllers achieve exceptional power density within rigorously constrained volumes. However, the compact layout design of these controllers constitutes a challenging NP-hard problem, characterized by strong multi-physics coupling—such as electromagnetic, thermal, and structural fields—and complex nonlinear constraints. Traditional meta-heuristic algorithms frequently suffer from premature convergence and struggle to balance global exploration with local exploitation. To address these challenges, the core contribution of this paper is the proposal of a novel Fractional-Order Anteater Foraging Optimization Algorithm (AFO), which is successfully applied to an established EHA controller layout optimization model. At the algorithmic level, by incorporating the Grünwald–Letnikov fractional derivative, the algorithm exploits the inherent memory property of fractional calculus to dynamically adjust the search step size and direction based on historical evolutionary information, thereby preventing stagnation in local optima. At the engineering application level, a high-fidelity mathematical model of the EHA controller is established, comprising 11 design variables and 10 critical physical constraints, including parasitic inductance minimization, thermal radiation efficiency, and electromagnetic interference (EMI) isolation. Extensive validation against the CEC2005 and CEC2022 benchmark functions demonstrates the superior convergence accuracy and stability of the AFO algorithm. In a specific EHA case study, the proposed method reduced the controller volume by 33.9% while strictly satisfying all multi-physics constraints, compared to traditional methods. Furthermore, a physical prototype was fabricated based on the optimized layout, and experimental tests confirmed its stable operation and excellent thermal performance. The results validate the efficacy of incorporating fractional calculus into bio-inspired algorithms to solve complex, high-dimensional engineering optimization problems. Full article