As the Internet of Things (IoT) grows, securing IoT edge devices has become increasingly critical, with threats becoming more sophisticated and frequent. This paper presents a novel security architecture that integrates Lightweight Virtualization (LV) with enhanced Trusted Execution Environments (TEEs), designed specifically to strengthen the security of IoT edge devices. Using ARM TrustZone technology, the proposed approach creates a secure execution environment capable of meeting the real-time performance requirements of industrial IoT applications. The architecture provides end-to-end security through embedded virtualization and trust mechanisms, ensuring protection from hardware to application layers and reducing the risk of unauthorized access and data breaches. Results from rigorous experiments demonstrate the superior performance of the proposed architecture compared to existing security frameworks. The experimental results indicate that the proposed approach offers a 40.93% average latency reduction over existing methods. Furthermore, the proposed approach offers a 19.19% average throughput improvement and a 33.65% reduction in average energy over existing methods.

Although swarm intelligence optimization algorithms, such as simulating biological bionic behaviors or natural laws have been relatively mature, there are relatively few algorithms considering multi-graph network evolutionary behaviors and the algorithms combining graph network structure with biomimetic behaviors are worth studying. In this paper, a multi-graph network population optimization algorithm with migration and best hunter crossover strategies was proposed for cross-field applications. The gorgeous central radial multi-graph matrices were rotated and deformed to change different formations while hunting prey. The global graph population of a strong group was adopted to explore prey in a large range and the local graph population of a weak group was adopted to guard food in a small range near their prey or home. The migration strategy was aimed at reducing overexploitation by hunters and the best hunter crossover strategy was aimed to retain the excellent genes of the best hunter while also preserving the vitality of new individuals. Furthermore, the proposed algorithm was applied to open-source function optimization problems, and extended to four engineering applications and design problems such as multi-sector aviation scheduling, flexible workshop scheduling optimization, unmanned aerial vehicle routing optimization of oil plants in three-dimensional maps, and power system bus type optimization achieving competitive results.

The aim of this study is to examine the dynamics of deposits, loans, and equity on the balance sheet of the bank under capital adequacy constraints. The intention is to provide a tractable framework for assessing solvency and regulatory policies. Therefore, a nonlinear continuous-time model was developed with logistic growth, credit risk, and capital adequacy conditions. The model was calibrated using monthly data for Indonesian commercial banks from 2022 to 2024, and the parameters were estimated using particle swarm optimization. The results showed that the model replicates observed trajectories with mean absolute percentage errors below 2.1% to confirm its empirical validity. The simulations showed that stricter capital requirements slowed equity growth while moderate requirements supported long-run capitalization. A time-varying capital adequacy policy was formulated as an optimal control problem, and the Pontryagin maximum principle was applied to derive an optimal regulatory path. The results showed that adaptive regulation stabilized capitalization while limiting policy costs. The trend reflected the value of the continuous-time control theory in financial regulation.

This study introduces a novel two-stage stochastic model of mean value exposed to conditional risk to allocate locations and to calculate the flow of materials and manufactured goods in a multi-level, multi-product supply chain. In this model, distributors and suppliers face potential disruptions and could spend money to prevent them. The suggested model considered several sources of uncertainty, such as transportation costs, final customer demand, and the possibility of disruptions at distribution centers and suppliers. The model used the conditional risk-exposed value and the risk-aversion coefficient to control for the risk caused by significant deviations from expected values. The designed model was transformed into a single-level linear programming model using a Monte Carlo simulation. Finally, the model was implemented through a numerical example, and its sensitivity analysis was conducted. The results of the model show that increasing the risk-aversion coefficient led to a decrease of more than 20% in the objective function across all confidence levels for the test problem, indicating the effectiveness of the proposed two-stage stochastic model in proactively mitigating disruptions.

The increasing power demand, transmission line congestion, and increasing electricity traffic necessitate the effective implementation of demand-side management (DSM) strategies to improve energy efficiency and sustainability. This research presents an optimized DSM framework for large power consumers in the Western Cape municipality, utilizing particle swarm optimization (PSO) integrated with machine learning improved prediction algorithms to achieve peak clipping and reduce peak load power demand under real-time pricing conditions. The developed algorithms were validated using actual energy consumption data from large industrial customers in the Western Cape province. Simulation results indicate that the PSO-driven DSM framework significantly reduces peak demand, improves the load factor, and offers substantial cost savings compared to conventional load management techniques. This study highlights the potential of intelligent optimization methods to support municipalities and major energy users in adopting more flexible, affordable, and sustainable energy consumption practices.

Understanding and accurately modeling the dynamics of climate-related processes is essential for predicting and mitigating the effects of global warming. This study introduces a fractional order atmospheric model that simultaneously captures the interactions among three key variables: permafrost thaw, atmospheric temperature, and greenhouse gas concentration. The model was formulated using the Atangana–Baleanu–Caputo fractional derivative, allowing for the inclusion of memory effects that are critical in climate dynamics. To solve the resulting nonlinear fractional differential equations, we constructed an operational matrix of the Atangana–Baleanu fractional integral operator based on Haar wavelets. Using Haar series expansions and operational matrices, the system was transformed into an objective function. This objective function was then minimized using differential evolution optimization to determine unknown Haar coefficients. The proposed method was validated against traditional numerical and predictor–corrector methods, with theoretical analysis confirming existence, uniqueness, and a provable upper bound for the approximation error. Numerical experiments under various parameter settings demonstrated the high accuracy, efficiency, and flexibility of the method. These results highlight the potential of fractional order modeling as a powerful framework for analyzing complex environmental systems and improving climate prediction models.

Mathematical modeling of epidemics is a cornerstone in the study and response to the spread of diseases and related processes across various domains. However, classical models generally do not describe such memory effects properly and are computationally inefficient, which restricts their applicability or predictive accuracy. To address these issues, we introduce a new approach to epidemic modeling using our newly proposed fractional-order differential equations, which are endowed with the Atangana–Baleanu system to describe long-range dependencies and nonlinear characteristics more accurately than the traditional Caputo system. To address this, we develop physics-informed neural networks and Fourier-based artificial intelligence-driven surrogate solvers, which are computationally efficient without compromising accuracy. To actuate intervention policies in a dynamic fashion, we also incorporate a hybrid control mechanism integrating the use of reinforcement learning with classical mathematical optimization to facilitate adaptive policymaking that benefits from data. Unlike existing work, our framework is rigorously evaluated on real-world epidemiological datasets from the World Health Organization and the Centers for Disease Control and Prevention, and tested extensively for out-of-the-box adaptability to cybersecurity (cyber malware), social rumor, and financial contagion problems. We also propose a data-free generative model (Fair4Free) that improves fairness, privacy, and utility in synthetic dataset generation, allowing its use even for constrained-data settings. Experimental evidence indicates that our holistic approach enhances the accuracy of predictive performance compared to baselines, with both lower computational cost and cross-domain generalizability to unprecedented settings. Finally, we set a new state-of-the-art for EpiModel by end-to-end training on fair data.

The bearing capacity of piles in soil is determined by both the mechanical properties of the soil and the method of pile installation. The widespread implementation of pile foundations in offshore oil and gas field development has highlighted significant deficiencies in the current domestic scientific, methodological, and regulatory approaches for evaluating pile–soil interaction. This study addresses the key issues and limitations in calculating bearing capacity for commonly used drilled-in and precast piles. For combined drilled-in piles, the existing methodology inaccurately assumes that the hydrostatic pressure exerted by the cement slurry on the borehole walls remains unchanged after hardening, leading to erroneous estimations. In the case of precast metal piles, the use of standardized regulatory tables results in substantial discrepancies compared to actual performance, particularly at depths exceeding 35 m, where these methods become completely inapplicable. Furthermore, the dynamic method outlined in building regulations-used to predict the bearing capacity of short precast piles driven using mechanical or hydraulic hammers in offshore environments-produces results with unacceptable margins of error. This method is also unsuitable for longer piles due to its inherent limitations. The root causes of the limitations in existing methods for evaluating the load-bearing capacity of pile foundations have been systematically investigated. Based on this analysis, the theoretical framework for a new calculation methodology has been developed. By integrating comprehensive laboratory data, a revised approach is proposed that significantly enhances the reliability and accuracy of the estimated bearing capacity, ensuring closer alignment with actual field performance. The bearing capacity and settlement of pile foundations for offshore hydraulic structures were computed and analyzed with consideration of the soil’s plastic deformation behavior.

Sustainable manufacturing systems require intelligent methods to balance economic performance with environmental responsibility. This research presents a digital twin-fuzzy multi-objective optimization framework for simultaneously managing cost, energy consumption, and waste in sustainable manufacturing. In this framework, fuzzy logic is used to model data uncertainty, a digital twin is used to obtain real-time data from the manufacturing process, and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used to generate a Pareto front and analyze the relationships between economic and environmental objectives. The proposed model was tested in 10 simulated scenarios based on digital twin data. The results showed that the proposed framework maintained the service level above 95%, reduced the total cost by 14% and the amount of waste by 18% compared to the baseline. Pareto front analysis also showed that although there is a relative conflict between economic and environmental objectives, this conflict is controllable. Also, sensitivity analysis revealed that energy ceiling and machinery efficiency have the greatest impact on the sustainability and profitability of the system. Overall, the proposed framework provides a reliable, quantitative decision-making tool for managers and policymakers on the path to green and sustainable production.

This study investigates a new subclass of analytic and univalent functions in the open unit disk, through the convolution of normalized analytic functions with a generalized Erdélyi-Kober fractional integral operator. The main objective is to define a new subclass TS(β, γ) related with the normalized form of the Erdélyi–Kober fractional integral operator K^ϑ_δ and explore its geometrical properties. This study obtains sharp coefficient bounds and geometric characteristics such as growth, and distortion properties. Furthermore, convexity, close-to-convexity, radii of and starlikeness, extremal functions, and inclusion relations are determined. These results contribute to the broader understanding of defined subclass within geometric function theory and provide a mathematical foundation for modelling phenomena in fractional calculus, conformal mapping, and applied engineering contexts. The study also highlights limitations associated with the operator parameters and suggests extensions to numerical and control-based models for future investigation.

Fixed point theory stands as a fundamental pillar in nonlinear functional analysis, being essential for proving the existence of solutions for nonlinear differential and integral equations. Krasnoselskii’s hybrid fixed point theorem, which combines the Banach contraction principle with Schauder’s theorem, is a pivotal contribution. Recent efforts have focused on refining and relaxing the conditions of this theorem. This study aims to extend the theoretical framework of Krasnoselskii-type fixed point theorems to address a broader and more general class of nonlinear operator equations within a Banach algebra setting. It also seeks to establish rigorous conditions for the existence (and uniqueness, where possible) of solutions. The approach involves developing local variants of the classic Krasnoselskii fixed point theorems. We performed a comparative analysis of previous studies, introduced modifications to the operator equations to relax restrictive assumptions, and theoretically generalized the theorems to accommodate a complex structure involving four operators. To validate the results, they were applied to a nonlinear functional integral equation within the Banach space C[0,1]. We successfully generalized existing results by incorporating the Hölder continuity condition, which is less restrictive than the standard Lipschitz condition. The unified theoretical framework led to the establishment of a comprehensive set of theorems and corollaries covering a wide class of operator equations such as: $A x^{(\rho 2)} B x^{\rho 1}+C x^{(\rho 3)} D x^{\rho 1}=x$. Our results provide less restrictive local existence conditions and wider applicability in the analysis of complex mathematical systems.

Despite the proven effectiveness of measles vaccines, suboptimal coverage and changing public behavior continue to pose challenges for eradication efforts worldwide. This study develops a fractional-order compartmental model to capture measles transmission dynamics while accounting for memory effects and adaptive behavioral responses to vaccination campaigns. Using Caputo fractional derivatives, the model reflects the non-local and history-dependent nature of disease spread more realistically than classical integer-order models. Four time-dependent control strategies-early newborn vaccination, adult catch-up immunization, administration of a second vaccine dose, and early treatment of exposed individuals-are incorporated and optimized through Pontryagin’s Maximum Principle adapted for fractional systems. A sensitivity analysis of the basic reproduction number shows which parameters have the biggest effect on the potential for an outbreak. Numerical simulations demonstrate that fractional dynamics significantly modify infection peaks, outbreak duration, and total intervention costs compared to classical models. The results emphasize that integrating memory effects and behavioral feedback can enhance the design of vaccination programs and inform more cost-effective public health policies for measles mitigation.

We present a Lyapunov-based framework for analyzing continuous-time accelerated optimization dynamics with time-dependent inertia and damping. By explicitly designing Lyapunov functions that account for varying inertia, we rigorously characterize convergence rates of the objective function, achieving exponential or polynomial acceleration beyond the classical O(1/t²), even in the absence of strong convexity. Building on this foundation, we introduce a variational extension using conformable (fractional) derivatives in the Lagrangian formulation, replacing the classical velocity term with a time-weighted fractional velocity. This approach systematically modulates the system’s effective inertia and damping, providing a principled mechanism to balance acceleration and stability, reduce oscillations, and interpolate smoothly between strongly damped gradient flows and momentum-driven dynamics. The resulting framework unifies Lyapunov analysis and fractional variational modeling, offering flexible, theoretically grounded design principles for fast and stable accelerated optimization.

This study addresses the critical challenge faced by organizations in selecting an optimal subgroup of decision-making units (DMUs). Such a selection procedure can significantly influence efficiency, profitability, and strategic development. Recognizing the limitations of existing methods in handling inexact data and incorporating managerial preferences, this study proposes a novel framework that integrates data envelopment analysis (DEA) with binary linear programming models. The model applies belief-degree–based representations of uncertainty to capture imprecise inputs and outputs. For this model, two solution approaches-namely, chance-constrained programming and expected value approaches-were developed. These approaches are suitable for real-world applications using standard optimization software. The effectiveness of the proposed method was validated through a case study in Iran’s petrochemical industry, where it successfully identified the optimal technology for a new refinery unit while balancing efficiency and profitability under uncertainty. This work is the first study in the literature to combine DEA and binary linear programming under belief-degree–based uncertainty for DMU selection, offering a systematic, practical, and computationally efficient solution, with recommendations for future research to explore alternative uncertainty modeling techniques and broader industrial applications.

Urban color landscapes play a significant role in shaping perceptual experience and street vitality. We proposed a style-based generative adversarial network 2 (StyleGAN2)-inspired generative framework for creating urban colorscapes and quantitatively assessing their vitality. The approach integrated advanced data preprocessing, generator–discriminator architecture, and hyperparameter optimization using a non-saturating logistic loss function. Vitality was evaluated through three chromatic indicators-saturation, contrast, and diversity-and validated against behavioral (pedestrian volume) and socioeconomic (point-of-interest density) data via correlation analysis (r = 0.47–0.68). The model achieved theoretical convergence (Fréchet Inception Distance < 15) and optimality, while ablation experiments with a deep convolutional GAN, Wasserstein GAN with gradient penalty, and StyleGAN3 confirmed its superior generative performance. The synthesized images exhibited an 18.2% increase in saturation and a 10.5% increase in diversity relative to real-world scenes, suggesting a strong positive association with urban vitality, as established in our correlation analysis. Computational efficiency was enhanced through mixed-precision training, reducing total processing time. Empirical and perceptual validations confirmed the framework’s robustness, offering a reproducible pathway for artificial intelligence-driven urban color planning.

Early detection of acute lymphoblastic leukemia (ALL) is crucial for improving survival outcomes in children. Manual diagnosis through microscopic examination is often time-consuming and subject to human error. This study presents an automated classification framework for pediatric ALL using a fine-tuned Residual Network (ResNet)-50 deep learning architecture. The model was trained and validated on 15,135 segmented blood smear images collected from 118 pediatric patients in the publicly available ALL IDB Version 2 dataset. Data augmentation and patient-wise splitting were applied to ensure model generalization and prevent data leakage. The fine-tuned ResNet-50 achieved a mean classification accuracy of 99.60%, with precision, recall, and F1-score of 99.45%, 99.40%, and 99.42%, respectively, outperforming baseline convolutional neural network models. Statistical validation (p < 0.0015) confirmed that these performance improvements are highly significant. This study highlights the potential of ResNet-50 for reliable, automated, and reproducible leukemia diagnosis, offering clinical decision support for early detection and treatment planning.

Retinal vessel segmentation is essential for the diagnosis and treatment planning of retinal diseases, yet remains challenging due to weak edges, tiny branches, and complex background textures. In this paper, we propose FracSegNet, a deep segmentation network that integrates fractional-order modeling at the preprocessing, feature extraction, and loss levels to improve the continuity and robustness of retinal vessel extraction. First, a Grünwald–Letnikov fractional differential operator is used to generate multi-directional edge responses, which are concatenated with the original fundus image to form an augmented multi-channel input. Second, adaptive fractional-order convolution blocks are embedded into a U-Net–like encoder–decoder architecture, where learnable order weights dynamically fuse integer-order and fractional-order responses, enabling simultaneous modeling of local details and long-range dependencies. Third, a composite loss is designed by combining Dice loss, total variation (TV) regularization, and a fractional gradient constraint that enforces consistency between the fractional-order gradients of the prediction and the ground truth. Experiments on the DRIVE, STARE, and CHASE DB1 datasets demonstrated that FracSegNet achieved competitive or superior performance compared with state-of-the-art methods, with F1 scores above 0.83 and clear improvements in edge continuity and fine-branch preservation. These results indicate that fractional-order modeling provides an effective and generalizable paradigm for segmenting weak edges and delicate vascular structures in medical images.

Imprecision, uncertainty, and conflicting criteria often complicate the process of identifying the optimal conclusions in real-world decision-making scenarios. This paper suggests a novel multi-criteria decision-making (MCDM) framework that combines a hybrid logarithmic precursor chain-driven objective weighting–preference ranking organization method for enrichment of evaluations technique with linear Diophantine fuzzy sets to address uncertain frameworks. The selection of the location of a Sustainable Emergency Service Station and the selection of an investment portfolio are two real-world and socially significant decision-making challenges where traditional MCDM approaches fail to address the uncertainties. Our suggested fuzzy-based paradigm demonstrates the adaptability of both infrastructure design and financial decision-making. The results provide the optimal solutions based on our requirements, even under unpredictable conditions. The outcomes of sensitivity analysis and comparative analysis demonstrate how well the suggested approach handles ambiguous and imprecise data, particularly when expert opinions are presented in a linguistically or incompletely articulated manner. This work provides a solid, scalable, and precise method for resolving MCDM issues in the face of ambiguity, offering improved support to decision-makers in a range of fields.

Fractional-order multi-agent systems with singular dynamics and time-varying network structures have gained increasing attention due to their ability to model complex interconnected processes with memory effects and algebraic constraints. In this paper, a novel adaptive pinning control framework for fractional-order singular multi-agent systems under switching topologies is proposed to achieve leader-following consensus. The proposed method simultaneously handles memory-dependent fractional dynamics, algebraic constraints from system singularity, and changing network connectivity, thereby addressing important limitations of traditional methods. By using a distributed adaptive protocol that only needs a small percentage of agents to be pinned, the technique dramatically lowers control complexity without sacrificing performance. Numerical simulations showed the framework’s practical superiority over currently existing methods in terms of convergence rate and robustness, while analytical results based on fractional Lyapunov theory established rigorous stability conditions that account for system uncertainties. Through an integrated approach to managing entangled fractional, singular, and network dynamic characteristics, these contributions enhance the control of intricate multi-agent systems. The proposed framework explicitly handles switching topologies through average dwell-time conditions and jointly connected graphs, providing rigorous stability guarantees under dynamic network changes.

A highly efficient and accurate numerical method for systems of fractional differential equations (FDEs) with rational order is presented in this paper. Rational power functions and rational Taylor series projection are utilized to obtain approximate solutions. Rational semi-smooth spaces are introduced, and the regularity of solutions in these spaces is established. A series of theoretical results, such as the existence and uniqueness of solutions, properties of the rational Taylor series and its remainder term, and an operational matrix approach, are derived. It is proven that the numerical solution is exact when the exact solution is a rational power series, and the approximate solution is shown to be the rational Taylor series projection of the exact solution. The convergence of the method is analyzed. The efficiency of the proposed method is demonstrated through numerical experiments, which show significant improvements in computational time compared to existing methods.