In this paper, Ulam’s stability of neutral fractional stochastic differential equations (NFSDEs) with sub-fractional Brownian motion (sfBm) is studied. Existence and stability results are established using fixed point theory, semigroup theory, and fractional calculus in a stochastic setting. We modify unstable impulses into stable impulses in the signal transformation of the cell tissue trajectory. Numerical simulations are provided to verify the obtained results. Fractional components are used to construct a fractional-order analogue circuit model for an artificial tissue homeostasis circuit, which is relevant to the application features. The proposed circuit offers several advantages for framing effective cell populations, including (i) predicting the death of β cells at the microscopic level for type 1 diabetics, (ii) regenerating the dead cells through stem cells, and (iii) achieving stable signal transformation between β cells and stem cells.
Renewable distributed generation (RDG), notably solar and wind energy, is increasingly integrated into distribution networks (DNs) to enhance sustainability, meet rising demand, and improve grid reliability. This study proposes a coordinated planning framework that jointly optimizes RDG siting/sizing and DN expansion using a hybrid Analytic Hierarchy Process–genetic algorithm (AHP–GA). Multi-objective goals—minimizing active power losses, reliability-related costs, and annual equipment investment—are scalarized using AHP-derived weights and solved through a chromosome-segmentation GA that reduces the search space and accelerates convergence. The method was validated on a modified IEEE 37-node radial distribution system, demonstrating substantial techno-economic benefits: total cost reductions exceeding 25%, approximately 75% reduction in active power losses, and about 40% improvement in reliability indices. A comparative assessment of the IEEE 69-bus system further underscored the approach’s efficiency, achieving an active power loss of 16.88 kW (a 92.50% reduction) and 112.67 s of CPU time, outperforming alternative metaheuristics. After the integration of DGs, both reliability indices improved significantly, resulting in reductions of 40.27% in System Average Interruption Duration Index (SAIDI) and 58.84% in Energy Not Served (ENS) annually. The results indicate that coordinated RDG–DN planning yields DNs that are more economical, reliable, and operationally robust than those from sequential or uncoordinated strategies.
The growing energy consumption, increasing demand for efficient cooling systems, energy preservation in clean energy technology, cooling technology, and chemical engineering, and the applications of nanofluids and non-Newtonian fluids have attracted the attention of researchers and scientists in fluid mechanics. Because this demand cannot be accommodated in current systems using fluids of low thermal conductivity, fluids such as nanofluids with high thermal conductivity are used to improve cooling systems. Therefore, the combined study of the interactions among solar radiation, heat generation, and an inclined magnetic field in a two-phase Buongiorno nanofluid model coupled with a non-Newtonian Williamson fluid model, considering shrinking and stretching wedges along a flat plate and a full wedge, was conducted in the present study. The transformed differential equations were solved using MATLAB’s bvp4c solver. The results show that increasing values of the Williamson fluid parameter, heat generation parameter, and inclined magnetic field parameter lead to a decrease in the velocity field for both the shrinking and stretching wedges along a flat plate and the full wedge under an inclined magnetic force . There is an increase in the temperature profile with increasing thermophoresis parameter and solar radiation parameter. The nanoparticle volume fraction increases with increasing values of the thermophoresis parameter for both cases of a wedge along a flat plate and a full wedge. A grid-independent test was performed to ensure that the solutions are grid-independent and that convergence of the solutions was maintained. The current results are compared with existing published results, which validates the accuracy of the present solutions.
Controlling the number of tumor cells remains a fundamental challenge in oncology due to the complex, nonlinear dynamics of tumor-immune interactions, extreme parameter scaling, and clinical constraints such as drug toxicity and the unidirectional nature of therapeutic interventions. To address these difficulties, this paper introduces a novel methodology for tumor growth control by leveraging the space of hyperbolic functions (HFs). We investigate a nonlinear model describing the dynamic interaction between effector cells and tumor cells. First, we design a stabilizing feedback control within the HFs framework, formulated as a hyperbolic tangent state feedback law. A Lyapunovbased analysis rigorously proves that this controller ensures global asymptotic stability of the desired equilibrium, where the tumor cell population is eradicated. Numerical simulations demonstrate that the proposed stabilizer drives divergent tumor growth to zero with a rapid convergence rate across various initial conditions. Furthermore, we formulate and solve an optimal control problem to simultaneously minimize the tumor cell population and the dose of a chemotherapeutic agent. The resulting optimality system, derived from Pontryagin’s Minimum Principle, is efficiently discretized and solved using a numerical scheme based on hyperbolic function approximations and Legendre-Gauss-Lobatto collocation points. Simulation results confirm the efficacy of this approach, illustrating a trade-off between tumor eradication and drug usage that can be tuned via the objective function’s weighting parameters. The findings collectively establish the space of hyperbolic functions as a powerful and efficient tool for both stabilization and optimal control in complex, nonlinear oncological models, offering a promising framework for designing therapeutic strategies.
The current study addresses the stability analysis in fractional-order fuzzy networked control systems with actuator faults and uncertainties. In contrast to existing studies on networked control systems, we carry out a comprehensive analysis using H∞ control for fractional-order networked control systems with distributed delays, aiming to improve system performance and robustness against denial-of-service attacks while accounting for actuator faults. A fuzzy controller is first designed for uncertain fractional-order fuzzy networked control systems with external disturbances. Subsequently, sufficient conditions based linear matrix inequalities (LMIs) are established using Lyapunov-Krasovskii functionals to ensure the asymptotic stability of the closed-loop system. The effectiveness of the proposed strategy is numerically validated using MATLAB® with different parameter settings. Finally, the comparative results show that the proposed method yields less conservative results than existing approaches.
Cold ironing reduces ship emissions in ports, but reliable renewable-based shore power requires effective energy management. This paper presents a deep deterministic policy gradient (DDPG)-based energy management system (EMS) for a photovoltaic (PV)–wind–battery energy storage system (BESS) cold-ironing direct current (DC) microgrid designed to supply renewable shore power to berthed ships. The proposed system consists of 2 MW PV arrays, a 1 MW permanent magnet synchronous generator wind turbine, a 1 MWh BESS, a regulated 1,000 V DC bus, a shore-side power conversion unit, and a backup grid interface activated only in case of failure of the standalone renewable energy sources/BESS system. A complete dynamic model was developed in MATLAB/Simulink to evaluate system performance under normal operation, renewable-power shortage, excess-generation conditions, and realistic Alexandria Port meteorological data. A conventional rule-based EMS was first implemented as a baseline controller to coordinate renewable generation, battery charging/discharging, PV power limitation, and DC-bus regulation. Then, a DDPG-based EMS was developed to generate continuous battery-control actions and supervise PV and wind operating conditions under variable renewable generation. The results show that the proposed PV–wind–BESS system maintained the DC-bus voltage close to its 1,000 V reference while reliably supplying the cold-ironing load. Compared with the conventional EMS, the DDPG-based EMS provided smoother battery response, improved renewable-source coordination, and reduced voltage fluctuations during critical shortage and excess-generation cases. The Alexandria Port case study further validates the performance of the proposed DDPG-based EMS under realistic operating conditions for renewable-powered cold ironing in Mediterranean and North-African coastal ports.
Machine learning-based intrusion detection systems (IDS) are commonly selected based on conventional validation or development metrics, although such criteria may not sufficiently reflect robustness against unseen attack families or suitability for resource-constrained Internet of Things and edge environments. This study proposes learned acquisition and reconstruction optimization (LARO)—IDS (LARO-IDS), a family-leakage-aware robust multi-objective optimization framework for model selection in Internet of Things intrusion detection. Instead of selecting the model that only maximizes conventional predictive performance, LARO-IDS jointly considers development macro-F1, mean cross-family robustness, worst-family behavior, robustness variability, and prediction latency in the candidate-selection objective, while training time and model size are retained as additional deployment-cost indicators for final comparison. Candidate models were evaluated using a model-selection evaluation subset and a leave-one-attack-family-out robustness protocol, then ranked using a weighted-sum scalarization of normalized objectives, with the results further supported by Pareto-efficiency analysis. Experiments on the CICIoT2023 dataset show that conventional score-based selection favors RF_03_regularized, which achieved the highest macro-F1. In contrast, LARO-IDS selects RF_01_fast, which preserves nearly identical predictive performance, with only a −0.0015 macro-F1 difference, while achieving slightly higher mean cross-family F1 scores across attack families. The LARO-selected model also reduces training time by 49.49%, prediction latency by 46.36%, and model size by 50.12% compared with the conventionally selected model. Sensitive analysis of objective weights further shows that RF_01_fast remains selected under balanced, performance-priority, robustness-priority, and edge-priority scenarios. These results demonstrate that robust IDS model selection should integrate family-leakage-aware robustness and latency-aware deployment cost rather than relying solely on conventional predictive performance.
Irrigation management in modern agriculture faces simultaneous challenges, including water scarcity, climate uncertainty, and the need for long-term sustainability. In this study, an integrated framework for real-time irrigation control is presented, in which a digital twin is not merely used as a monitoring or simulation tool but is directly embedded in the decision-making and control loop through an agent-based fuzzy multi-objective optimization mechanism. Unlike conventional smart irrigation approaches that rely on static thresholds or offline optimization, the proposed framework enables adaptive, context-based decision updates by continuously integrating physical system feedback into a dynamic optimization engine. The decision-making agent, by simultaneously assessing soil, climate, and plant growth conditions, generates irrigation policies that balance water consumption, crop growth, and environmental sustainability requirements under fuzzy uncertainty. Experimental results show that using dynamic feedback in the digital twin framework improves the multi-objective performance index by more than 12% compared to the static state and significantly reduces control fluctuations. Convergence, stability under uncertainty, and parameter sensitivity analyses also indicate that the proposed framework can establish a sustainable balance across water resource utilization, crop yield, and environmental considerations. The findings indicate that this approach can provide a practical and reliable platform for transitioning to smart, adaptive, and sustainable irrigation systems.
Topology awareness and scalable, adaptive network control have become critical with the development of 5G/6G, the Internet-of-Things, vehicular networks, and edge computing. Traditional rule-based and centralized networking models are unable to support dynamic topologies, heterogeneous traffic models, and demands with strict quality-of-service requirements. Structural and topological dependencies are encoded using graph neural networks (GNNs) and combined with deep reinforcement learning (DRL) to make decisions sequentially. Exploiting rewards is an avenue toward intelligent end-to-end network optimization. This review is a systematic examination of modern GNN–DRL models implemented in routing, congestion control, chaining of service functions, vehicular communication, and the optimization of optical networks. It also highlights their performance strengths, including topology awareness, cross-topology generalization, high sample efficiency, and high scalability, as well as their weaknesses, such as inference overhead, inconsistent benchmarking practices, low real-time deployability, and sensitivity to noisy or partial state observations. The main findings of this review are: (i) a coherent taxonomy of GNN-based, DRL-based, and hybrid GNN–DRL effective designs; (ii) comparative analysis of algorithms, architecture components, and learning pipelines; (iii) generalized performance trends in major areas of intelligent networking; and (iv) a collection of grounded research directions to be followed in the future, lightweight architecture, transfer learning pipeline, fault tolerant learning, and unified evaluation frameworks. Finally, this review focuses on enabling resilient infrastructure through intelligent, scalable, and autonomous end-to-end networking solutions.
Distributed denial-of-service (DDoS) attacks have become a major threat to the stability of critical infrastructure networks, where even short service disruptions can lead to severe operational and economic consequences. To better capture the complex dynamics of these attacks, we extend an existing epidemic-based DDoS model by employing the fractal–fractional (FF) Atangana–Baleanu (AB) operator, which effectively accounts for memory effects, network heterogeneity, and irregular traffic patterns commonly observed in cyber environments. Within this framework, we establish the existence and uniqueness of solutions and examine the Ulam–Hyers stability of the proposed system. The local stability of both infection-free and endemic equilibria is assessed to identify the conditions under which the network can maintain normal operation. Numerical simulations are performed using the Adams–Bashforth method for various combinations of fractional and fractal orders. The results show that the FFAB formulation captures slower decay, extended memory, and more realistic transient dynamics than its classical counterpart. These findings demonstrate that incorporating FF dynamics offers a more flexible and accurate representation of DDoS propagation and quarantine based mitigation, providing valuable insights for enhancing the resilience of modern cyber-infrastructure systems.
The outbreak of the COVID-19 pandemic has highlighted the need for advanced mathematical tools capable of accurately describing complex disease transmission dynamics. Fractional calculus has emerged as a powerful modeling framework due to its ability to incorporate memory effects and nonlocal behavior, which are intrinsic to infectious disease spread. This review provides a comparison of solutions obtained through the application of various fractional operators, including Caputo, Caputo–Fabrizio, Atangana–Baleanu derivative in Caputo sense, and fractal-fractional derivatives with power-law, exponential decay, and Mittag–Leffler memories. Key analytical properties such as positivity, boundedness, equilibrium analysis, basic reproduction number estimation, existence and uniqueness of solutions, Hyers–Ulam–Rassias stability, and chaos control are systematically discussed. The review further highlights the application of fractional models in capturing the effects of vaccination, quarantine, hospitalization, environmental transmission, and control interventions. By consolidating recent theoretical and applied advances, this work demonstrates the superiority of fractional-order models over classical integer-order approaches in reproducing real world COVID-19 dynamics. The presented review serves as a valuable reference for researchers and policymakers seeking robust and flexible modeling strategies for epidemic analysis and control.
Retailers increasingly need decision-support tools to manage unsold inventory under operational and fiscal constraints. In this paper, we develop a reverse supply chain (RSC) model for retailers under profit–loss budgetary limitation. The retail RSC consists of multiple stores, a warehouse, and multiple vendors. Each store carries inventory that is not selling as hoped, and they want to get rid of these unwanted products to replace the space with more productive items. Our model considers two options for how a store can get rid of these products: the retailer can send the products to its warehouse if there is demand at other stores, or send them back to their vendor if there are available vendor funds. However, the retailer operates under a predetermined profit–loss budget that should be utilized as closely as possible within the fiscal cycle. The budgetary limitation is the result of profit–loss that will be incurred due to relocating products within and out of its supply chain system. This budgetary limitation, also known as the “P&L effect” in industry, is decided a year prior to an RSC activity for financial, planning, and/or taxation reasons. We model this problem as a mixed integer linear program and solve test problems using CPLEX. We then develop a heuristic solution algorithm and compare the CPLEX solution results and times with our heuristic. We summarize useful insights into our heuristic and how it can be further developed for similar optimization problems with budgetary constraints. Eventually, we outline future research topics and suggestions for RSC models for retailers.
In designing urban multiday personalized tourism itineraries, hotel selection and the frequency of hotel changes are key factors influencing tourists’ satisfaction with the itinerary. To investigate the mechanism by which this factor affects itinerary satisfaction, this study proposes an urban personalized tourism itinerary design model that incorporates the frequency of hotel changes. A branch-and-bound algorithm is applied to obtain optimal tourism itineraries. Based on customer satisfaction theory, this study proposes a satisfaction evaluation model for personalized urban tourism itineraries across three dimensions: economy, convenience, and experience, and performs a satisfaction analysis of optimal tourism itineraries with varying hotel change frequencies. This study conducted case-based experiments using tourism data from Chongqing. The results indicate that personalized tourism itineraries based on a high-frequency hotel-change model outperform those of a low-frequency model across several indicators: average transportation costs decrease by ¥95, total distance travelled decreases by 47 km, and total rest time increases by 123 minutes. As luggage transfer services between hotels become more widespread, hotel selection and the frequency of hotel changes will have a greater impact on satisfaction with personalized urban tourism itineraries.
Classical Data Envelopment Analysis (DEA) models are traditionally built on the assumptions of certain and non‑negative data. In contrast, real‑world applications frequently involve negative values and epistemically uncertain information. Uncertainty theory offers a rigorous mathematical alternative to probability and fuzzy set theory for handling such indeterminacy. This study extends the Range Directional Measure (RDM) model by integrating uncertainty theory to simultaneously address negative data and uncertain environments. The proposed uncertain RDM model is operationalized and validated using an empirical dataset from the Tehran stock market, where traditional efficiency metrics often fail due to volatile financial ratios and negative returns. The findings demonstrate that the proposed framework yields more robust efficiency scores and provides actionable insights for stock evaluation under uncertainty. This integration advances the DEA literature by bridging the gap between performance measurement and uncertainty theory in negative‑data contexts.
The focus of this article is to propose two different versions of the Heisenberg uncertainty principle related to the fractional Fourier transform (FrFT). The first version is directly derived using the basic connection between the traditional Fourier transform (FT) and the FrFT, and the second is derived by exploiting time differentiation property and Parseval’s formula for the FrFT. In addition, a weighted uncertainty inequality related to this transformation is investigated. As a simple illustration of the use of the obtained results, we design the fractional characteristic function. An inequality describing the relation between the probability density function and its fractional characteristic function is presented.
Minimal surfaces have zero mean curvature. These surfaces have the smallest possible area for a given boundary curve, and are widely used in engineering, biological design, and architecture. In this study, we present a method to construct minimal surfaces using trigonometric Pythagorean hodograph (PH) curves. First, we generate PH trigonometric curves, and subsequently apply the Weierstrass representation to derive the corresponding minimal surface. The constructed PH curve serves as a boundary isoparametric curve of the surface. We analyze key geometric properties such as symmetry, surface area and mean curvature. Representative examples are provided to demonstrate the effectiveness of the proposed method.
Utilizing the (q, τ)-nabla fractional operator, we develop a discrete-time Dengue transmission model incorporating memory and time-scale deformation effects. Stability, endemic equilibrium, and bifurcation behavior are analyzed through Jacobian eigenvalue methods and fractional threshold conditions. A Lyapunovbased feedback strategy and a memory-weighted optimal control framework are introduced to regulate infected and hospitalized populations. Necessary optimality conditions are derived using a generalized Pontryagin maximum principle adapted to the (q, τ)-fractional setting. Numerical simulations confirm the theoretical results and demonstrate the influence of the parameters q, τ, and α on memory dynamics and intervention efficiency. The proposed framework provides a flexible approach for modeling and controlling epidemic systems with nonlocal memory effects.
Annual Wellness Visits (AWVs) generate large volumes of clinical and laboratory data that can support predictive healthcare analytics. However, the high-dimensional nature of healthcare datasets often introduces redundant and irrelevant variables, which may negatively affect model performance and computational efficiency. This study proposes a hybrid framework that integrates metaheuristic feature selection techniques with machine learning and deep learning models to improve predictive analysis using AWVs data. Three optimization algorithms, namely Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Harris Hawks Optimization (HHO), were employed to identify informative feature subsets from a dataset containing 2,518 patient records and 53 clinical attributes. The selected features were subsequently used to train several machine learning classifiers and deep learning architectures, including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Recurrent Neural Network (RNN) models. Experimental results demonstrate that metaheuristic optimization effectively reduces dataset dimensionality while maintaining strong predictive performance. The feature selection process successfully identified compact subsets of clinically relevant variables, leading to improved model efficiency and reduced computational complexity. Comparative analyses indicate that optimized feature subsets improve classification performance across multiple learning algorithms, while deep learning models exhibit high training capability on the AWVs dataset. The findings highlight the importance of combining feature selection with advanced predictive models to improve healthcare data analysis and support data-driven clinical decision-making. The proposed structure provides an effective approach for handling high-dimensional healthcare datasets and offers a foundation for the development of intelligent clinical decision-support systems. Future work will focus on validating the structure using larger multi-center datasets and incorporating explainable artificial intelligence techniques to improve model interpretability and clinical applicability.
With the growing reliance of multi-area interconnected power systems on communication networks for large-scale data transmission, sensing, and control, network constraints can impair transient performance. This work develops a unified distributed fault-estimation framework based on a radial basis function neural network (RBF-NN) for multi-area interconnected power systems, addressing both communication constraints and actuator faults. We construct an augmented system by integrating the fault dynamics into the system model, and a distributed observer is developed to simultaneously estimate the system states and fault dynamics. The unknown fault effect is approximated by a radial basis function neural network (RBF-NN). A projection-based adaptation law ensures bounded parameter estimation under modeling uncertainties. State and fault estimates are updated using quantized measurements transmitted over networked channels, maintaining accuracy despite time-varying delays and disturbances. Sufficient stability and performance conditions are established by Lyapunov analysis and LMI conditions, guaranteeing exponential stability of the observer error dynamics and prescribed performance bounds under bounded time-varying delays and quantization effects. A three-area case study is presented, and precise state and fault reconstruction are shown for nominal, delayed, faulted, and worst-case scenarios. The proposed scheme is compared with a quantized H∞ estimator under actuator faults, time-varying delays, and quantization. The peak deviations of |Δω|, |ΔPtie|, and |ΔPmech| are reduced approximately 33%, 50%, and 27%, respectively, while maintaining bounded system states and neural weights.
