Search Results (1,602)

Rooftop rainwater harvesting (RWH) offers a practical adaptation option for Mediterranean cities where water scarcity is amplified by seasonal rainfall and climate variability. This study reports early findings from a simplified monthly water balance screening model for a typical residential building, driven by ERA5-Land monthly precipitation for Antalya and İzmir (Türkiye). Scenarios cover roof areas of 250–3000 m² and practical tank capacities of 2–100 m³ under a fixed non-potable demand of 0.20 m³/day. The model tracks monthly storage dynamics and supply demand in order to compute demand coverage and monthly reliability (i.e., fraction of months in which full demand is met). Reliability-based storage thresholds (≥0.80) are derived for four evaluation windows (1996–2010, 2011–2025, 1996–2025, 1950–2025) to explore climate sensitivity. In parallel, a guideline-style sizing which is consistent with the Turkish rainwater harvesting guideline is implemented using a three-day storage rule based on the wettest month potential. To enable a like-for-like comparison, the collection losses are harmonized by setting loss to 0.10 in the simulation and efficiency to 0.90 in the guideline method. The results show stable thresholds for Antalya but stronger period sensitivity in İzmir. They also quantify cases where guideline sizing does not achieve the target reliability under dry season constraints. This approach supports the rapid, climate-aware pre-design of small- to medium-scale urban RWH systems. Full article

This study introduces a Caputo fractional-order version of the SEIRS-V model to investigate the spreading dynamics of worms within wireless sensor networks. Traditional integer-order worm propagation models describe the instantaneous evolution of network states; however, they do not adequately account for memory and hereditary characteristics that may influence the transmission dynamics. Consequently, their ability to represent realistic network behavior can be limited in systems where past states affect current propagation patterns. The framework divides sensor nodes into susceptible, exposed, infectious, recovered, and vaccinated classes, while explicitly incorporating worm transmission rates, temporary loss of immunity, and the impact of preventive security measures under limited resource conditions. A detailed theoretical examination is performed, covering the existence, boundedness, and uniqueness of solutions of the fractional-order system. The coupled nonlinear fractional system is solved semi-analytically by means of the Fractional Reduced Differential Transform (FRDT) technique. To confirm accuracy and robustness, the identical system is also discretized and solved using the finite difference scheme (FDS). Unlike previous studies on worm propagation models in wireless sensor networks, which are mainly limited to equilibrium point analysis and qualitative investigations without deriving explicit solutions, the present work develops an approximate semi-analytical solution for the fractional-order SEIRS-V system using the FRDTM. Comparisons between the two solution sets demonstrate excellent agreement and high precision. Numerical outcomes are presented through a series of 2D graphical profiles that illustrate the time-dependent behavior of each compartment and reveal the sensitivity of worm propagation and suppression to variations in the fractional order and key model parameters. The integrated theoretical and computational findings underscore the strong protective role of vaccination in mitigating worm outbreaks and offer valuable guidelines for strengthening cybersecurity measures in wireless sensor networks. Full article

The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, particularly how the fractional order $\beta$ influences these regimes. This study addresses these gaps through a comprehensive, multi-method dynamical analysis of a representative nonlinear oscillator embodying key FWBK features. Three-dimensional attractor visualizations, return maps, and surrogate data tests demonstrate a transition from quasi-periodic toroidal attractors to fully developed chaos via torus breakdown, confirming that observed complexity originates from deterministic nonlinearity. Poincaré sections reveal multistability and KAM-type structures, where coexisting attractors depend on initial conditions, while increasing noise progressively disrupts coherent dynamics. The OGY control method effectively stabilizes unstable periodic orbits across chaotic regimes with minimal perturbation, and Lyapunov analysis indicates that stochastic forcing attenuates chaos while enhancing dissipation. The Fokker–Planck framework shows that noise reshapes probability landscapes, driving transitions from unimodal to bimodal distributions. Comparative analysis of SINDy, JMAP and VBA highlights trade-offs in interpretability, computational efficiency, and uncertainty quantification, while an integrated Bayesian–PCE–Sobol approach quantifies parametric uncertainty and reveals time-dependent sensitivity variations. Additionally, the overlapping of soliton solutions extracted via the enhanced modified Sardar sub-equation method reveals structural relationships among soliton families and their stability under interaction. Soliton branches that maintain high overlap under noise correspond to stable regimes, while those losing coherence indicate the onset of chaos. Furthermore, while the reduced dynamics in $\eta$-space are independent of $\beta$, the fractional order controls spatial compression and temporal scaling in physical coordinates, directly influencing observable wave localization. These results imply that fractional effects can modify chaos transitions, support controllability through OGY, and influence noise–instability interactions depending on $\beta$. This framework provides a robust, transferable methodology for analyzing and controlling nonlinear oscillatory systems under deterministic and stochastic conditions, with direct applications to FWBK-based models in coastal engineering, fiber optics, and quantum interference systems. Full article

We propose a fractional-order cancer virotherapy model based on Caputo derivatives to investigate the temporal interactions among tumor cells, viruses, and immune response components. The existence and uniqueness of the solutions for the proposed model are rigorously studied. The proposed model is capable of tracking the temporal dynamics of uninfected and infected cancer cells, free oncolytic virus, and several components of the immune response. To determine the analytical solutions of the resulting nonlinear fractional-order system, we utilize the Temimi–Ansari method (TAM). The convergence and accuracy of the method are confirmed via error analysis and numerical simulation carried out in MATHEMATICA. It is observed that the fractional order plays a prominent role in controlling the temporal dynamics of the cancer–virus–immune system, leading to a reduction in the number of infected cancer cells due to virotherapy. On the other hand, the immune response is vital for controlling cancer growth. Full article

Photovoltaic (PV) generation and electric vehicle (EV) charging infrastructure are changing the dynamic behavior of current power systems, especially in terms of voltage stability and LVRT capabilities. In this work, 50% PV penetration on a modified Kundur two-area power system was tested to mitigate transient instability under severe fault circumstances. With PV units running at unity power factors under steady-state conditions, 50% PV penetration was defined relative to the system’s total active load demand. A steady-state power-flow study ensured generation–load balance before MATLAB/Simulink dynamic simulations. Controllable reactive power compensation was used as an EV aggregator on Bus 7. We constructed and evaluated a genetic algorithm (GA)-optimized fractional-order proportional–integral–derivative (FOPID) controller with a traditional PID controller utilizing identical optimization conditions. An inter-area tie-line critical three-phase fault was applied and removed after 100 ms to evaluate system performance. While the GA-PID controller increased transient performance, it did not restore system stability. Instead, the GA-FOPID controller provided superior dynamic support by restoring Bus 7 voltage to 0.9–1.1 pu within 250 ms after fault clearance and maintaining about 95% LVRT compliance. The suggested controller also reduced rotor angle oscillations and enhanced inter-area damping. Fractional-order control increased EV aggregators’ reactive power response during transient shocks. Thus, in renewable-energy-dominated power systems, the GA-FOPID-controlled EV support technique may improve voltage stability and LVRT compliance. Full article

Traditional human motion prediction methods attempt to discover the relationship between observed and future motion sequences. However, due to the dynamic complexity of human motion, existing methods cannot fully capture the interrelationships among motion sequences, and their performance remains unsatisfactory. In this work, we propose a novel Two-stage Refinement (TSR) framework for human motion prediction. It consists of two branches: (i) a traditional motion prediction branch for preliminary prediction, and (ii) an auxiliary refinement branch designed to estimate and compensate for the preliminary prediction errors. In this way, we can obtain better prediction performance than with traditional one-stage methods. To further bridge the gap between predicted results and groundtruth, we introduce a novel fractional-order differential loss function in this work. Existing methods use only integer-order differences to capture instantaneous state changes, often failing to account for the long-range temporal dependencies in human motion. By contrast, the inherent memory effect of the fractional-order differential loss function can account for long-term dependencies and enable precise tuning of high-order trajectory derivatives, thus yielding more physically realistic motion sequences with minimal error accumulation. Comparative experiments demonstrate that our proposed Fractional Optimization-based Two-stage Refinement Framework (FOTSR) outperforms most existing works on three benchmarks (including Human3.6M, CMU-Mocap, and 3DPW). Full article

In this study, a detailed analytical-numerical study of the complex modified Korteweg–De Vries (mKdV) model with truncated M-fractional derivative is carried out to investigate the effects of the fractional order on nonlinear wave propagation. The fractional partial differential equation is solved by an appropriate fractional traveling wave transformation, which transforms it into a nonlinear ordinary differential equation. Two very powerful analytical methods are then used: the modified sub-equation method and the Kumar–Malik method, which give the exact closed-form solutions. The obtained semi-analytical numerical approximations are then obtained from the Differential Transformation Method (DTM). Bright and dark solitons, kink-type waves, periodic and rational solutions, exponential solutions, and Jacobi elliptic functions are found for a variety of parametric regimes. Explicit compatibility conditions and parametric constraints, which control the amplitude, width, and propagation, are derived. The DTM approximations are found to converge to the exact solutions with good accuracy, and the absolute errors are almost negligible, which validates the accuracy of the approximations and reliability of the solution. The three-dimensional visualizations of surface plots, two-dimensional profiles, and contour visualization further illustrate the dispersive dynamics and stability properties. Significance: This study shows that the truncated M-fractional derivative is a good operator to model memory-dependent nonlinear wave propagation. A new precise solution and reliable validation methods have been obtained for high-dimensional fractional nonlinear evolution equations in the hybrid analytical-numerical framework, which can be useful in plasma physics, nonlinear optics, and complex media. The present study contains restrictions for constant coefficients, a specific parametric regime, one fractional derivative definition, and experimental validation is not included. Future directions are limitations on constant coefficients, specific parametric regimes, one fractional derivative definition, and experimental validation is not included. The approach is to be extended in the future to variable coefficients, other fractional operators (Caputo, Riemann–Liouville), and to higher-order nonlinearities, and then to be experimentally tested in optical or plasma systems. Full article

In this research, based on Adomian decomposition method (ADM), we construct true fractional-order differential equations. Due to the boosting function brought by the sine function, the system can output infinite coexistence attractors on y–z planes. In particular, this grid effect becomes increasingly obvious as the fractional order increases. Based on this boosting grid idea, in combination with the fractal dynamics, we construct some fractal patterns, e.g., Koch snows. These fractal diagrams all present grid fractal shapes. And then, we design a grid image encryption algorithm. This algorithm is proven to have higher security. The combination of chaos and fractals explores a new research direction. It provides new ideas for research in related fields. Full article

The main objective of this study is to investigate smoking dynamics, identify the most influential factors governing smoking behavior, and develop effective intervention strategies through the integration of fractional-order modeling, sensitivity analysis, optimal control theory, and artificial neural networks (ANNs). A nonlinear fractional-order compartmental model is formulated by dividing the population into potential smokers, light smokers, heavy smokers, and quit smokers. The smoking reproduction number is derived to characterize the transmission and persistence of smoking behavior within the population. To determine the impact of model parameters on smoking dynamics, both normalized forward sensitivity analysis and global sensitivity analysis based on Latin Hypercube Sampling (LHS) with Partial Rank Correlation Coefficient (PRCC) are performed. The obtained results identify the most sensitive transmission and progression parameters and demonstrate their important role in shaping smoking prevalence within the community. Furthermore, the classical integer-order model is compared with the fractional-order formulation, where the fractional model provides a more realistic description due to its ability to incorporate memory and hereditary effects associated with smoking behavior. An optimal control framework involving awareness and treatment strategies is further introduced to investigate effective smoking reduction policies. The numerical results demonstrate that awareness campaigns reduce smoking initiation, while treatment interventions increase smoking cessation, and the combined implementation of both strategies produces the most significant reduction in smoking prevalence. The consistency between the sensitivity analysis and optimal control results further supports the reliability of the proposed framework. Numerical simulations are carried out to analyze the qualitative and quantitative behavior of the system under different epidemiological scenarios. In addition, an ANN-based computational framework is employed as an efficient numerical tool to accurately approximate the complex dynamics of the proposed fractional-order smoking model with very low prediction error. Overall, the present study provides a comprehensive mathematical and computational framework for understanding, analyzing, and controlling smoking behavior within a population. Full article

We investigate dynamic weighted fractional information-theoretic measures for linear stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/2,1)$. Motivated by recent constructions of fractional Deng entropy and building upon explicit Gaussian solutions and closed-form fractional moments derived in previous work, we establish fully analytical expressions for the Shannon entropy, Rényi entropy, Tsallis entropy, extropy, and a continuous weighted fractional entropy $\mathbb{E}\left[X_t^p(-\log p_{X_t}\left(X_t\right))\right]$ for $p\ge 0$, expressed directly in terms of known fractional moments without density estimation. All derived measures share a universal asymptotic scaling law growing as $H\log t$, establishing a precise quantitative link between long-memory effects and information dynamics. The weighted fractional entropy further reveals remarkable structural properties as a function of the weighting order p, exposing a dual role of long memory on the system’s informational content. As a concrete application, we characterize anomalous diffusion in aging soft materials through an explicit critical time linking maximal uncertainty to the memory exponent H and the macroscopic aging rate. All results are validated through extensive Monte-Carlo simulations, demonstrating excellent agreement with the closed-form expressions across a wide range of Hurst exponents H and weighting orders p. Full article

Volcanic gas and isotope time series are indirect observables of coupled magmatic and hydrothermal dynamics. We formulate a reduced integer–fractional model in which ordinary differential equations describe deep recharge, pressure, gas-phase volatile inventory, and source mixing, whereas Caputo equations describe shallow hydrothermal pressure, thermal excess, gas pathway effectiveness, permeability, and scrubbing. Under explicit local regularity and admissibility assumptions, the mixed-order Volterra problem is locally well-posed and the physically admissible state set is positively invariant. We derive componentwise dissipative estimates and state conditions for global continuation under bounded trajectories and analyze finite-interval consistency with the integer-order limit and local stability of a frozen commensurate hydrothermal linearization. Conservative observation equations link hidden states to gas ratios, fluxes, and isotope ratios. The inverse problem is treated diagnostically; global identifiability is not claimed. Local sensitivity screening, Fisher information concepts, and scalar recovery tests are used only as preliminary local diagnostics of information content under known or misspecified forcing. Synthetic demonstrations and a reference forward solver illustrate how hydrothermal memory and sulfur scrubbing can reshape carbon dioxide/sulfur dioxide (CO₂/SO₂) anomalies before site-specific calibration. Full article

This study investigates the Mittag–Leffler-type stability properties of fractional perturbed systems with respect to their unperturbed counterparts by incorporating initial time differences into the analysis. In contrast to many existing studies in which initial time effects are neglected, the proposed framework explicitly considers time shifts together with the memory-dependent nature of fractional-order systems. Using Caputo fractional derivatives and Lyapunov-type functionals, new sufficient conditions are established for the stability behavior of perturbed systems relative to the corresponding unperturbed systems under shifted initial times. The obtained results extend existing stability criteria by simultaneously addressing fractional memory effects, perturbation terms, and variations in the initial time. To illustrate the applicability and effectiveness of the theoretical findings, representative examples, numerical simulations, graphical comparisons, and global error analyses are presented. The numerical part is based on the Caputo framework and is further supported by benchmark comparisons involving Riemann–Liouville and shifted Grünwald–Letnikov approaches. The proposed results provide a useful framework for the stability analysis of memory-dependent dynamical systems arising in engineering and applied sciences. Full article

A new fractional dynamic sliding mode control (FD-SMC) framework is introduced to reduce chattering in the control of fractional-order chaotic systems. In this method, chattering is eliminated by placing a fractional integrator before the system control input. As a result, the augmented system has a higher dimension than the original system, meaning that additional states are introduced. Effective control therefore requires identifying or estimating these new states or the corresponding plant model. To address this issue, a robust optimal fractional loop-transfer-recovery observer (ROF-LTRO) is developed. Furthermore, the key advantage of sliding mode control (SMC)—its invariance to matched uncertainties—is often lost in many plants such as chaotic systems, because many of them contain mismatched uncertainties. To restore and extend the invariance property, multiple sliding surfaces combined with a virtual control input are employed. In addition, the proposed FD-SMC and ROF-LTRO do not rely on prior knowledge of uncertainty bounds, which is beneficial for practical implementation. Then, a two-stage design procedure based on two-surface definition is presented, and simulation results are provided for the extended fractional Duffing–Holmes chaotic system (EF-DHCS) under both matched and mismatched uncertainties. Full article

The growing need for secure image transmission across public networks requires robust encryption algorithms. Traditional chaos-based image ciphers typically have a small key space, weak avalanche behavior, or are susceptible to differential cryptanalysis. To overcome such inadequacies, this paper suggests a new adaptive image cryptosystem that combines a fractional-order memristive chaotic engine and a non-linear hybrid encryption kernel. The system uses piano-inspired feedback; the keystream generator dynamically adapts to the previously encrypted pixel, enabling powerful Cipher Block Chaining (CBC)-style chaining and content-dependent diffusion. A four-dimensional memristive system is solved by the use of fractional-order calculus, which gives an ultra-large key space (>10⁸⁰) and very high sensitivity to initial conditions—confirmed by a positive largest Lyapunov exponent (1.7199). The encryption kernel maps the traditional Exclusive OR (XOR) with the reversible two-step operation: the modular addition of the plaintext with the first keystream byte and the XOR with the second keystream one, both of which increase non-linearity and confusion. Large-scale experiments with six standard 256 × 256 colour images indicate almost ideal entropy (7.9994), Number of Pixel Change Rate (NPCR) which is 99.62, Unified Average Changing Intensity (UACI) which is 33.43, correlation coefficients are near to zero, very low Gray-Level Co-occurrence Matrix (GLCM) homogeneity (≈0.017) and high contrast (≈4843) and low energy (≈0.006 The ciphertext passes seven National Institute of Standards and Technology (NIST) SP-800-22 statistical tests, is extremely sensitive to keys (a perturbation of 1 × 10⁻¹⁴ alters >99.6% of ciphertext) and resists chosen-plaintext and known-plaintext attacks. Decryption has linear time complexity O(N), and average encryption and decryption times are 3.40 s and 2.75 s for 256 × 256 images. The proposed cryptosystem provides an attractive security–performance trade-off that can be used in high-security systems like medical image protection, privacy-preserving multimedia transmission, and secure cloud storage. Full article

This paper presents a methodology for synthesizing static state feedback controllers utilizing a Fractional-Order Performance Index. Linear Quadratic Regulators are designed using integer-order integral weighting functions. In the proposed approach, fractional-order calculus is utilized to introduce an additional degree of freedom in controller synthesis, enabling enhanced shaping of the plant’s dynamic properties. The controller gains are obtained by solving a fractional Riccati-like equation, through which the temporal weighting properties inherent to fractional integration are embedded into a static feedback matrix. This formulation is a minimalist control structure suitable for implementation on resource-constrained hardware. The proposed method is validated via rapid control prototyping on an industrial NI PXIe platform and an analog third-order plant. Performance evaluation using Integral Absolute Error and Integral Absolute Control metrics demonstrates that the fractional order serves as a flexible tuning parameter, providing an alternative trade-off between settling time and control effort. Furthermore, frequency domain sensitivity analysis demonstrates the absence of resonant peaks and inherent attenuation of high-frequency measurement noise. As a result, the presented framework bridges fractional-order optimization techniques with industrial control platforms. Full article