Search Results (249)

Mass transfer–induced Marangoni convection in volatile binary liquids is commonly associated with the amplification of interfacial concentration disturbances, yet the localized evolution preceding the first visible convective cell remains difficult to quantify experimentally. Here, ethanol–water desorption in a confined quasi–two–dimensional cell with a 2 mm liquid thickness was investigated using quantitative Schlieren imaging. The apparent transient concentration field and interfacial concentration profiles were reconstructed to resolve the earliest observable stage of Marangoni onset. The early behavior depended strongly on the initial ethanol mass fraction. Low–concentration cases mainly exhibited Rayleigh plume structures, high–concentration cases developed Marangoni cellular structures too rapidly for reliable early–stage tracking, whereas intermediate–concentration cases provided a resolvable window before Marangoni cell formation. For an initial ethanol mass fraction of 8 wt.%, a localized interfacial onset site appeared before the first visible Marangoni convective cell. This event initiated two counter–propagating spreading fronts, enriched the swept interfacial region, and was followed shortly by visible Marangoni cellular structures within the redistributed region. The apparent surface tension gradient field exhibited a transient evolution, with an initial increase, followed by a decrease during spreading, and a subsequent increase upon front interaction. These results provide experimental reference data for the pre–cellular interfacial redistribution sequence associated with perturbation–driven Marangoni onset in confined ethanol–water desorption systems. Full article

In this paper, we investigate the practical exponential stability of a class of nonlinear systems governed by the tempered $\varpi$-Caputo fractional derivative. A new Lyapunov-based criterion is established to derive sufficient conditions ensuring $\varpi$-practical exponential stability. The obtained result is formulated in a general framework involving suitable growth bounds on the Lyapunov function together with a tempered fractional derivative inequality and a boundedness condition on a weighted integral term. The proposed theorem provides an explicit practical exponential estimate for the system trajectories and extends existing stability results that are available for standard fractional and tempered fractional systems. To demonstrate the applicability of the developed theory, two applications are presented. First, the general criterion is applied to a class of perturbed tempered $\varpi$-fractional systems, for which verifiable sufficient conditions are derived in terms of quadratic Lyapunov functions and perturbation bounds. Second, a state-feedback stabilization result is established for a class of nonlinear tempered fractional control systems, showing that the proposed theorem can be used as an effective tool for closed-loop practical exponential stabilization. Finally, numerical examples are provided to validate the theoretical developments and to illustrate the effectiveness of the proposed approach. An additional test case with ${\eta }_3>0$ is included to demonstrate the nontrivial range of Theorem 1. Furthermore, a socio-economic tempered fractional cobweb model is incorporated to show how the proposed criterion applies to price-adjustment dynamics with memory and persistent market perturbations. Full article

In this article, we use truncated M-fractional derivatives to analyze the bifurcation and chaotic behavior of and traveling-wave solutions to the Zhiber–Shabat equation. By introducing truncated M-fractional derivatives, the equation exhibits richer dynamic properties. Based on phase diagram analysis and dynamical system theory, the bifurcation behavior of the equilibrium point of a two-dimensional dynamical system is discussed. At the same time, the dynamical behavior of a two-dimensional dynamical system with periodic disturbances is considered, revealing the complex chaotic phenomena of the system under specific parameters. A planar phase diagram, a three-dimensional phase diagram, a sensitivity analysis, and a maximum Lyapunov exponent diagram of the perturbed two-dimensional dynamical system were employed. Furthermore, various forms of accurate analytical solutions were obtained through traveling-wave transformation and numerical simulation. The three-dimensional, two-dimensional, density, and polar coordinates of the solutions were plotted using mathematical software. The results indicate that the fractional order and system parameters have a significant impact on the morphology and chaotic characteristics of the solution. This study provides new theoretical insights into the nonlinear dynamics of fractional-order Zhiber–Shabat equations. Full article

This paper establishes a rigorous analysis of a coupled hybrid fractional differential system involving a generalized Hilfer operator under integral and antiperiodic boundary conditions. The existence and uniqueness of solutions are proved using Dhage’s fixed point theorem for existence and the Banach contraction principle for uniqueness. Furthermore, we establish Ulam–Hyers stability by deriving the following explicit and computable bound estimate: $\left(\begin{array}{c}\parallel \widehat{u}-u\parallel \\ \parallel \widehat{v}-v\parallel \end{array}\right)\le {(I-\mathit{\chi })}^{-1}\left(\begin{array}{c}{C}_1{ϵ}_1\\ C_2{ϵ}_2\end{array}\right)$, where $C_1$ and $C_2$ are positive constants depending on the system parameters, ${ϵ}_1,{ϵ}_2$ denote the perturbation bounds, and $\mathit{\chi }$ is the associated Lipschitz matrix. This formulation provides a more detailed stability description than scalar criteria, as it captures the interactions among the system components through the entries of $\mathit{\chi }$, leading to a more informative stability estimate. Two illustrative examples confirm the theoretical results and demonstrate their potential applicability for modeling real-world phenomena where memory effects are present. Full article

Reliable monitoring of hydraulic networks is essential for efficient and sustainable water management in agriculture. To address the growing need for intelligent, low-latency anomaly detection in such systems, we propose HydroNeuro, a domain-aware embedded framework that integrates hydraulic domain knowledge with data-driven neural inference for the real-time detection of leaks and obstructions. Rather than embedding physical equations directly into the learning objective, we leverage established hydraulic principles, including Bernoulli’s equation and the Darcy–Weisbach formulation, to structure the experimental design, interpret pressure–flow relationships, and ensure physical consistency of the learned representations. These principles confirm that pressure deviations induced by leaks or obstructions are causally explainable and measurable. We employ a fractional factorial design (FFD) to optimize valve activation combinations and sensor configurations during dataset acquisition, thereby reducing redundant experiments, water circulation, and energy consumption while limiting mechanical stress on system components. We deploy a lightweight neural network on an ESP32 microcontroller using TensorFlow Lite for Microcontrollers to enable energy-efficient, low-latency edge inference under severe hardware constraints. Our experimental validation on a laboratory-scale hydraulic testbed demonstrates anomaly detection accuracy exceeding 96%, with strong robustness under sensor noise and hydraulic perturbations. Compared to a multiple linear regression baseline, the proposed neural model reduces the prediction error from an RMSE of 0.58 to 0.12. By coupling physically consistent experimental modeling with embedded neural inference, HydroNeuro provides a scalable and practically deployable solution for autonomous hydraulic monitoring in precision irrigation and smart water distribution systems. Full article

Modern cyber–physical infrastructures rely heavily on alarm and notification systems to direct human attention when abnormal conditions occur. These mechanisms support timely and safe responses by informing operators and occupants about potential hazards. At the same time, research in human factors has shown that repeated or excessive alerts can weaken vigilance, slow reactions, and reduce confidence in warning systems. This behavioral pattern is commonly described as alarm fatigue. This paper examines how that vulnerability can be exploited intentionally. We refer to this adversarial strategy as alarm poisoning: the deliberate injection of false or misleading alerts in order to increase alarm pressure, erode trust in the monitoring infrastructure, and degrade organizational responsiveness over time. To study this process, we develop a stochastic Cybersecurity Dynamics model representing the interaction among attackers, defenders, alarm infrastructure, and a population of employees. Employee behavior is modeled through evolving trust and fatigue levels, while the overall system is formulated as a continuous–time Markov chain and simulated using the Gillespie Stochastic Simulation Algorithm. A Monte–Carlo campaign is used to analyze the resulting socio–technical dynamics under alternative attacker strategies. The study evaluates time-dependent trust, fatigue, and alarm-pressure trajectories, the distribution of times to behavioral collapse, and defender timing through Trust–Resilience–Agility–Mitigation (TRAM) metrics. The revised analysis also includes replication-sufficiency diagnostics, one-at-a-time sensitivity analysis, and threshold-robustness checks for the collapse criterion. The results show that false alarms with high perceived severity drive alarm pressure upward and degrade trust faster than nuisance-dominated campaigns, even when the total fake-alarm intensity is held constant across strategies. Collapse timing remains highly variable across stochastic realizations, and a non-negligible fraction of runs do not reach the collapse threshold within the simulation horizon. Sensitivity analysis indicates that the main qualitative ranking of attacker strategies is robust across most tested perturbations, with fatigue recovery and defender escalation emerging as particularly influential mechanisms. Overall, the findings support the view that alarm poisoning is a credible socio–technical attack vector and highlight the importance of rapid mitigation, robust alarm management, and human-centered defensive design in cyber–physical security systems. Full article

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

In this paper, we investigate the partial approximate controllability of a class of fractional diffusion control systems with three-parameter damping and nonlinear perturbations. First, based on the theory of $(\mu ,\nu ,\xi ,e,k)$-resolvent families developed in our previous work, we define the mild solution of the system. Then, by constructing a proper objective functional and using the strict convexity, we prove the existence and uniqueness of the minimal norm control. Furthermore, employing the Arzelà–Ascoli theorem and variational inequalities, we establish the precompactness of the solution family and derive the key controllability estimate. Finally, we provide an example to illustrate the effectiveness of our theoretical results. 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

This paper proposes and studies a new class of nonlinear nonlocal problem driven by a tempered Caputo-type fractional derivative with respect to an arbitrary smooth kernel. The novelty lies in treating a single nonlocal integro-delay setting that simultaneously couples an arbitrary kernel, exponential tempering, a delayed state, a lower-order distributed fractional memory term, and multipoint nonlocal initial data, rather than introducing a new fractional operator. The resulting problem can be viewed as a rigorous well-posedness prototype for hereditary systems with delayed feedback, tempered memory, and nonlocal initialization. First, an equivalent Volterra integral equation is derived. Then, the existence and uniqueness of solutions are obtained by the Banach contraction principle in a suitable Banach space of continuous functions. Next, a Picard successive approximation procedure is introduced and shown to converge uniformly to the unique solution, together with an explicit a priori error estimate. Moreover, a continuous dependence result is proved with respect to perturbations in the initial constants, the multipoint coefficients, and the nonlinear term. Finally, the main results are illustrated with two examples enhanced by graphs of explicit Picard approximations and convergence tables. 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

This critical review examines the evolution of mathematical modeling approaches for aerobic digestion processes in food industry waste management, highlighting their role in operational optimization and dynamic prediction. In recent years, increasing pressure for sustainable waste management, circular bioeconomy strategies, and process intensification in the food industry has accelerated the development of mathematical tools for describing complex biological treatment systems, making a critical synthesis of available modeling approaches particularly timely. Starting from mass conservation principles, simple kinetic models such as first-order and Monod models are analyzed. These models assume homogeneity and perfect mixing but fail to capture the heterogeneity of effluents rich in variable carbohydrates, proteins, and lipids. Structural limitations, including numerical rigidity, parametric non-identifiability, and idealized assumptions that underestimate spatial gradients and stochastic fluctuations, are examined. In continuous systems, coupled substrate–biomass–oxygen dynamics, washout phenomena, and extensions toward partial differential equations for representing real heterogeneity are explored. Structured models such as Activated Sludge Models (ASMs) incorporate multicomponent fractions but face parameterization challenges exacerbated by limited industrial data availability, as less than 25% of treatment plants currently employ formal modeling frameworks. Emerging paradigms include hybrid mechanistic–machine learning approaches for prediction under perturbations, multiscale modeling, and spatially explicit modeling. Unlike previous reviews that focus primarily on technological aspects of waste treatment, this study provides a critical comparison of modeling frameworks and their applicability to different food waste matrices. A classification table distributes approaches by food matrix, revealing the dominance of simple kinetics in composting and ASMs in activated sludge systems. Finally, a progressive model selection framework based on operational objectives is proposed, balancing model complexity with predictive robustness and experimental validation to support sustainable industrial adoption. Full article

In this article, we present a new approximate solution for blood nanofluid having gold nanoparticles as it flows near a stretching porous cylinder in fractal space. A Casson non-Newtonian magneto-bio-nanofluid flowing through a porous medium is considered a potential application in chemotherapy for eradicating cancer cells. Without the need for the nonperturbative approach, the proposed solution uses an alternative approach to dealing with nonlinear problems. This approach transforms the nonlinear cubic jerk model resulting from the simplification of the governing fractional partial differential equations into an equivalent linear formula. This approach is known as highly efficient linear approximation (HELA) or non-perturbation technique (NPT), and this represents a significant advancement over traditional perturbation methods in the analysis of non-linear systems. As a robust mathematical approach, it excels at handling a wide range of coefficient values, particularly in cases of clear nonlinearity. This study also utilized the masking technique simultaneously with HELA, which played a crucial role, as they simplify the complex dynamics of the system, making it more amenable to analysis. The numerical solution by the Runge–Kutta fourth-order (RK-4) method integrated with a shooting technique compared favorably with graphs drawn for the analytical solution from the proposed strategy HELA. The current results show that an increase in the fractal factors enhances the resistance to fluid motion, leading to a suppression of the velocity field. Physically, this often relates to the complexity of the medium or the fractal nature of the transport process, where higher fractal dimensions or factors can lead to slower diffusion or flow rates, like the role of porous media. Therefore, the current study has significant implications in the promotion of nanotechnology fields in medicine, particularly the use of gold nanoparticles in chemotherapy for the eradication of cancerous cells. Full article

Tripterygium glycoside tablets (TGT), a representative formulation derived from Tripterygium wilfordii Hook F, have limited clinical application due to adverse reproductive toxicity. In previous studies investigating the effects of TGT on chronic kidney disease (CKD), it was found that both TGT and its alkaloid-enriched fraction (AEF) induced testicular atrophy, suggesting that AEF may be the material basis for the reproductive toxicity of TGT. Therefore, the reproductive toxicity of AEF was investigated in depth. This study established a CKD rat model to investigate the toxic effects of TGT, AEF, and the non-alkaloid-enriched fraction (NAEF) on the reproductive system during CKD treatment. Network toxicology and metabolomics were combined to elucidate the underlying mechanisms of AEF-induced reproductive toxicity. The results showed that both TGT and AEF significantly reduced testicular index and sperm concentration, causing seminiferous tubule atrophy and disrupting the levels of testosterone (T), follicle-stimulating hormone (FSH), and luteinizing hormone (LH). Furthermore, TGT, AEF, and NAEF all significantly inhibited the proliferation of GC-1 cells. Network toxicology indicated that AEF modulates targets such as SRC, AKT, and HSP90AA1, thereby influencing pathways including the PI3K-AKT signaling pathway and pathways in cancer. Metabolomics obtained 89 differential metabolites of AEF, which were enriched in glycerophospholipid, linoleic acid, and arachidonic acid metabolism, a finding consistent with the constructed “metabolite–enzyme–reaction–gene” network. In summary, AEF exerts reproductive toxicity primarily by disrupting hypothalamic–pituitary–testicular axis homeostasis and perturbing glycerophospholipid, linoleic acid, and arachidonic acid metabolism. Full article

Sea-surface reflections and wind–wave motion render maritime channels strongly time-varying and statistically non-stationary, while nearshore deployments face sparse infrastructure and co-channel multiuser interference. This study integrates reconfigurable intelligent surfaces (RISs) with rate-splitting multiple access (RSMA) for joint online resource allocation. A physics-inspired time-varying channel model is established by embedding fractional Brownian motion-driven slow statistical drift and reflection-phase perturbations. With imperfect, delayed channel state information (CSI) and discrete RIS phase quantization, a proportional-fairness utility maximization problem is formulated to jointly optimize shore base-station precoding, RIS phase shifts, and RSMA common-rate allocation. To cope with strong non-convexity, high dimensionality, mixed continuous–discrete coupling, and partial observability, a fractal-aware recurrent robust Actor–Critic (FRRAC) algorithm is developed. FRRAC encodes short observation histories using a gated recurrent unit and incorporates a lightweight Hurst-proxy estimator to capture slow channel statistics for robust value evaluation and policy learning. Truncated quantile critics and mixed prioritized–uniform replay further improve value robustness, training stability, and sample efficiency. Simulation results show that FRRAC converges faster and more stably under both conventional and fractal non-stationary channel modeling, and outperforms representative baselines across the objective and multiple statistical metrics, validating its effectiveness for joint resource optimization in maritime RIS–RSMA systems. Full article