Fractals最新文献_第6页

FRACTAL-BASED DIGITAL TWINS FOR ENERGY SYSTEMS: A MULTI-SCALE MODELING PARADIGM FOR REAL-TIME OPTIMIZATION 基于分形的能源系统数字孪生：实时优化的多尺度建模范式

Fractals Pub Date : 2026-08-20 DOI: 10.1142/s0218348x26300072

MOHAMAD FANI SULAIMA,NORAZRYANA MAT DAWI,HANA SCHMIRLEROVA,HAMIDREZA NAMAZI

{"title":"FRACTAL-BASED DIGITAL TWINS FOR ENERGY SYSTEMS: A MULTI-SCALE MODELING PARADIGM FOR REAL-TIME OPTIMIZATION","authors":"MOHAMAD FANI SULAIMA,NORAZRYANA MAT DAWI,HANA SCHMIRLEROVA,HAMIDREZA NAMAZI","doi":"10.1142/s0218348x26300072","DOIUrl":"https://doi.org/10.1142/s0218348x26300072","url":null,"abstract":"Modern energy systems are increasingly shaped by renewable integration, distributed generation, and dynamic demand, creating nonlinear and multi-scale behaviors that are difficult to capture using conventional digital twin models. This paper reviews digital twin technologies and fractal-based modeling approaches in energy systems and proposes a novel fractal-based digital twin (FDT) framework. The proposed framework integrates fractal feature extraction, real-time digital twin synchronization, AI-driven prediction, and optimization-oriented control within a unified multi-layer architecture. Its novelty lies in using fractal descriptors, such as the Hurst exponent, fractal dimension, and multifractal features, to enrich system representation and support adaptive decision-making under dynamic operating conditions. Key challenges related to data quality, computational complexity, implementation barriers, and real-world validation are critically discussed. The findings indicate that fractal-enhanced digital twins can improve the scalability, robustness, and adaptability of digital twin applications for next-generation energy system optimization.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

TOWARD A UNIFIED FRACTAL-AI FRAMEWORK FOR SUSTAINABLE ENERGY SYSTEMS: A REVIEW AND FUTURE RESEARCH AGENDA 面向可持续能源系统的统一分形人工智能框架：综述与未来研究议程

Fractals Pub Date : 2026-08-20 DOI: 10.1142/s0218348x26300060

MOHAMAD FANI SULAIMA,NORAZRYANA MAT DAWI,MICHAL SCHMIRLER,HAMIDREZA NAMAZI

{"title":"TOWARD A UNIFIED FRACTAL-AI FRAMEWORK FOR SUSTAINABLE ENERGY SYSTEMS: A REVIEW AND FUTURE RESEARCH AGENDA","authors":"MOHAMAD FANI SULAIMA,NORAZRYANA MAT DAWI,MICHAL SCHMIRLER,HAMIDREZA NAMAZI","doi":"10.1142/s0218348x26300060","DOIUrl":"https://doi.org/10.1142/s0218348x26300060","url":null,"abstract":"The increasing complexity of sustainable energy systems, driven by the large-scale integration of renewable resources, distributed generation, and multi-energy infrastructures, has created significant challenges in modeling, prediction, and system optimization. Conventional approaches, which often rely on linear assumptions and isolated modeling techniques, are insufficient for capturing the nonlinear, multi-scale, and highly dynamic behavior of modern energy systems. In this context, fractal theory and artificial intelligence have emerged as powerful and complementary paradigms for addressing these challenges, where fractal analysis enables the characterization of scale-invariant dynamics and long-range dependencies, while AI provides advanced capabilities for prediction, optimization, and control. However, existing research largely treats these approaches independently, resulting in fragmented methodologies that limit their effectiveness in complex energy environments. To address this gap, this paper presents a comprehensive review of fractal-based modeling and AI-driven techniques in sustainable energy systems and proposes a unified FractalAI framework that integrates multi-scale analysis, data-driven intelligence, and system-level optimization within a cohesive architecture. The proposed framework enables enhanced representation of complex system dynamics, improved prediction of energy behavior, and adaptive control under uncertainty. The paper further identifies key challenges and outlines future research directions for developing intelligent, resilient, and scalable energy systems based on the integration of fractal theory and artificial intelligence.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"149 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

ON THE THEORY OF MULTIPLICATIVE CONFORMABLE FRACTIONAL INTEGRALS AND THEIR APPLICATIONS TO HERMITE–HADAMARD AND MACLAURIN-TYPE INEQUALITIES 关于乘型适形分数积分的理论及其在hermite-hadamard和maclaurin型不等式中的应用

Fractals Pub Date : 2026-08-19 DOI: 10.1142/s0218348x2650132x

ABDELGHANI LAKHDARI,MANAR A. ALQUDAH,FAHD JARAD,YAKUP YILDIRIM,THABET ABDELJAWAD

引用次数: 0

CRISIS REGIMES, TARIFF UNCERTAINTY, AND CROSS-ASSET ETF EFFICIENCY: A ROLLING MULTIFRACTAL ANALYSIS 危机机制、关税不确定性和跨资产etf效率：滚动多重分形分析

Fractals Pub Date : 2026-08-18 DOI: 10.1142/s0218348x26501380

FERNANDO HENRIQUE ANTUNES DE ARAUJO,ELIE BOURI

{"title":"CRISIS REGIMES, TARIFF UNCERTAINTY, AND CROSS-ASSET ETF EFFICIENCY: A ROLLING MULTIFRACTAL ANALYSIS","authors":"FERNANDO HENRIQUE ANTUNES DE ARAUJO,ELIE BOURI","doi":"10.1142/s0218348x26501380","DOIUrl":"https://doi.org/10.1142/s0218348x26501380","url":null,"abstract":"This paper examines the time-varying multifractal efficiency of nine US-listed Exchange-Traded Funds (ETFs) representing equities, bonds, real estate, commodities, gold, crude oil, and the US dollar. To this end, Multifractal Detrended Fluctuation Analysis (MFDFA) is applied to daily ETF logarithmic returns from March 2012 to February 2026, and full-sample estimates are complemented by rolling 500-trading-day windows advanced by 21 observations. The analysis distinguishes the pre-COVID period, COVID-19, the Russia–Ukraine war, the Israel–Hamas conflict, and the US tariff period associated with the second Trump administration. Efficiency is measured as the absolute deviation of the singularity-spectrum peak from the random benchmark 0.5. The full-sample ranking identifies the US dollar, gold, US government bonds, and commodities as the closest ETF exposures to the benchmark, whereas investment-grade bonds, real estate, high-yield bonds, and crude oil are more distant. Rolling estimates show that average inefficiency rises during COVID-19 and Russia–Ukraine, while the shorter Israel–Hamas endpoint window records lower average inefficiency in this ETF universe. Two-way clustered OLS regression indicates that mean event effects are not statistically significant after conservative dependence corrections, whereas bootstrap quantile regressions show upper-tail amplification: COVID-19, Russia–Ukraine, and US tariffs are most visible when ETF markets are already in high-inefficiency states. The findings support an adaptive view of ETF efficiency in which crisis and political-policy regimes affect the distributional tail of multifractal inefficiency more strongly than its conditional mean.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

VARIATIONAL PRINCIPLE OF THE FRACTAL RANGWALA–RAO EQUATION IN OPTICS AND QUANTUM SYSTEM 光学与量子系统中分形rangwala-rao方程的变分原理

Fractals Pub Date : 2026-08-17 DOI: 10.1142/s0218348x26501392

JING YANG,KANG-JIA WANG

引用次数: 0

SOLITON DYNAMICS IN FRACTIONAL BENJAMIN–BONA–MAHONY–BURGERS-TYPE EQUATIONS: A TWO-STEP LAPLACE ADAMS–BASHFORTH ALGORITHM WITH MACHINE LEARNING VERIFICATION 分数阶benjamin - bona - mahony - burgers型方程中的孤子动力学：带机器学习验证的两步Laplace adams-bashforth算法

Fractals Pub Date : 2026-08-17 DOI: 10.1142/s0218348x26501379

SHAHID HUSSAIN GURMANI,ZESHAN ASLAM KHAN,TAUSIF AHMAD,IMRAN SHAKIR,RANA MUHAMMAD ZULQARNAIN,IMRAN SIDDIQUE

{"title":"SOLITON DYNAMICS IN FRACTIONAL BENJAMIN–BONA–MAHONY–BURGERS-TYPE EQUATIONS: A TWO-STEP LAPLACE ADAMS–BASHFORTH ALGORITHM WITH MACHINE LEARNING VERIFICATION","authors":"SHAHID HUSSAIN GURMANI,ZESHAN ASLAM KHAN,TAUSIF AHMAD,IMRAN SHAKIR,RANA MUHAMMAD ZULQARNAIN,IMRAN SIDDIQUE","doi":"10.1142/s0218348x26501379","DOIUrl":"https://doi.org/10.1142/s0218348x26501379","url":null,"abstract":"This paper presents a comprehensive numerical investigation of the time-dependent fractional Benjamin–Bona–Mahony–Burgers (BBMB) equation, which governs nonlinear dispersive wave phenomena and admits stable soliton solutions that maintain their shape during propagation. We developed and compared three distinct computational frameworks for simulating soliton dynamics under fractional order operators: (i) a finite difference method employing discretization for the Caputo fractional derivative, (ii) a novel two-step Laplace Adams–Bashforth (TS-LAB) hybrid scheme that combines Laplace transformation with fractional predictor-corrector methodology, and (iii) a neural network (NN) incorporating fractional operator differentiation. The TS-LAB method demonstrates robust stability properties and improved computational efficiency for multi-term fractional partial differential equations (PDEs), utilizing Laplace transforms for accurate starting values and aiding soliton evolution over extended domains. The neural network implementation, optimized via the Levenberg–Marquardt algorithm, achieves exceptional convergence with a mean squared error of [Formula: see text] in only 12 epochs, while accurately capturing the characteristic shape-preserving property of solitary waves. Moreover, numerical experiments are conducted for both the fractional BBM and BBMB equations across varying fractional orders ([Formula: see text] to [Formula: see text]). Results reveal that as [Formula: see text] approaches unity, systematic amplitude reduction occurs alongside improved numerical accuracy, with the soliton profile remaining well-resolved despite amplitude attenuation. The BBMB equation exhibits a sharp error reduction for [Formula: see text], indicating optimal performance of the TS-LAB scheme near integer-order derivatives.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

AN INNOVATIVE GREY MODEL APPROACH WITH FRACTAL CALCULUS FOR FORECASTING RENEWABLE AND WASTE-BASED ELECTRICITY GENERATION 利用分形微积分的灰色模型预测可再生能源和废物发电

Fractals Pub Date : 2026-08-14 DOI: 10.1142/s0218348x26501355

MEHMET KOCABIYIK

{"title":"AN INNOVATIVE GREY MODEL APPROACH WITH FRACTAL CALCULUS FOR FORECASTING RENEWABLE AND WASTE-BASED ELECTRICITY GENERATION","authors":"MEHMET KOCABIYIK","doi":"10.1142/s0218348x26501355","DOIUrl":"https://doi.org/10.1142/s0218348x26501355","url":null,"abstract":"This study proposed and employed a Fractal Grey model to estimate the fraction of electricity produced from renewable and waste sources in Türkiye from 2010 to 2024. It was compared to the classical grey model and several nonlinear grey models and a sensitivity analysis was performed with different training–testing periods. The results indicate that the proposed model can effectively represent the small changes in the short and limited dataset and has a higher forecasting accuracy and more stable parameters than the other models. The traditional grey model and Discrete Grey model are both good at forecasting the trend, but they are slower to adjust to sudden changes than the Fractal Grey model. The sensitivity analysis also shows that the parameters of the Fractal Grey model are not sensitive to the changes of the training period, and the model is relatively robust to the changes of the range of data. Electricity generation projections for 2025–2030 generated by the model indicate that electricity generation by renewable and waste energy sources will share a bigger percentage of the total electricity generation in Türkiye. The results indicate that the Fractal Grey model is useful for energy planning and policy-making and can be a reliable model when data are limited and there is some uncertainty. In summary, the study offers a scientific reference for the energy transition strategies, capacity planning, and investment decisions that are taken in Türkiye, and also establishes the Fractal Grey model as an innovative approach that can easily provide accurate forecasts even with a short dataset.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

CASIMIR-INDUCED PULL-IN INSTABILITY AND NONLINEAR DYNAMICS IN FRACTAL RF MEMS: MATHEMATICAL MODELING AND ANALYSIS 分形mems中卡西米尔诱导的拉入不稳定性和非线性动力学：数学建模与分析

Fractals Pub Date : 2026-08-14 DOI: 10.1142/s0218348x26501331

ZIXUAN HUANG,DAN TIAN,XINGXING LV

{"title":"CASIMIR-INDUCED PULL-IN INSTABILITY AND NONLINEAR DYNAMICS IN FRACTAL RF MEMS: MATHEMATICAL MODELING AND ANALYSIS","authors":"ZIXUAN HUANG,DAN TIAN,XINGXING LV","doi":"10.1142/s0218348x26501331","DOIUrl":"https://doi.org/10.1142/s0218348x26501331","url":null,"abstract":"Radio-frequency microelectromechanical systems (RF MEMS) technology has developed rapidly in recent years and has been widely applied in communication systems, sensing devices, and other advanced electronic platforms. Motivated by the significant role of nanoscale effects, this paper investigates the influence of the Casimir force on pull-in instability in RF MEMS structures. A theoretical framework is first established by incorporating Casimir interactions into the classical MEMS formulation, leading to a Casimir RF MEMS model. To further capture multiscale geometric features, the model is extended into fractal space, resulting in a fractal Casimir RF MEMS formulation. Within this unified framework, the pull-in dynamics are systematically analyzed and compared with the conventional model to show the impact of nanoscale physics and fractal geometry. The results demonstrate that the Casimir force substantially alters the instability behavior by lowering the critical pull-in actuation threshold and modifying the stability characteristics, while the fractal structure further affects the evolution of the pull-in process. In addition, He’s frequency formulation is applied to obtain numerical periodic solutions of the governing equations, enabling an effective characterization of nonlinear oscillatory responses. Overall, this study provides a mathematical framework for Casimir- and fractal-induced effects in RF MEMS and offers new insights into the design and optimization of next-generation micro- and nano-electromechanical systems.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"354 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

FRACTAL-BASED MODELING OF ENERGY SYSTEM CASCADING FAILURES: A REVIEW AND CONCEPTUAL FRAMEWORK FROM LOCAL DISTURBANCES TO SYSTEMIC COLLAPSE 基于分形的能源系统级联失效建模：从局部扰动到系统崩溃的回顾和概念框架

Fractals Pub Date : 2026-08-11 DOI: 10.1142/s0218348x26300059

MOHAMAD FANI SULAIMA,ONDREJ KREJCAR,HAMIDREZA NAMAZI

{"title":"FRACTAL-BASED MODELING OF ENERGY SYSTEM CASCADING FAILURES: A REVIEW AND CONCEPTUAL FRAMEWORK FROM LOCAL DISTURBANCES TO SYSTEMIC COLLAPSE","authors":"MOHAMAD FANI SULAIMA,ONDREJ KREJCAR,HAMIDREZA NAMAZI","doi":"10.1142/s0218348x26300059","DOIUrl":"https://doi.org/10.1142/s0218348x26300059","url":null,"abstract":"Cascading failures in modern energy systems represent one of the most critical challenges for system reliability and resilience, as localized disturbances can propagate across interconnected networks and lead to large-scale systemic collapse. Conventional modeling approaches, including deterministic contingency analysis, dynamic simulation, agent-based models, branching-process models, and complex-network methods, have provided valuable insights into cascading failure mechanisms; however, they may face limitations in consistently representing scale-invariant behavior, long-range correlations, and multi-scale propagation across complex energy infrastructures. In this context, fractal theory provides a useful framework for modeling cascading failures by characterizing related but distinct features such as fractal behavior, scale invariance, power-law event statistics, long-range dependence, and possible self-organized critical dynamics. This paper presents a comprehensive review of cascading failure mechanisms in energy systems and examines the application of fractal-based approaches for modeling failure propagation across multiple scales. A novel fractal-based cascading failure framework is proposed, integrating multi-scale disturbance characterization, fractal propagation modeling, and system-level collapse analysis. The framework enables improved understanding of how local disturbances evolve into systemic failures, enhances early warning capabilities, and supports resilience-oriented system design. The paper further identifies key challenges and outlines future research directions for developing scalable, predictive, and adaptive models of cascading failures in next-generation energy systems.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

ANALYSIS OF THE TWO-DIMENSIONAL WAVELETS TECHNIQUE FOR THE COUPLED NONLINEAR VARIABLE-ORDER TIME-FRACTIONAL SINE–GORDON EQUATIONS IN COMPLEX DYNAMICAL SYSTEMS 复杂动力系统中耦合非线性变阶时间分数型正弦戈登方程的二维小波分析

Fractals Pub Date : 2026-08-07 DOI: 10.1142/s0218348x26501215

S. PRAMANICK,S. SAHA RAY

{"title":"ANALYSIS OF THE TWO-DIMENSIONAL WAVELETS TECHNIQUE FOR THE COUPLED NONLINEAR VARIABLE-ORDER TIME-FRACTIONAL SINE–GORDON EQUATIONS IN COMPLEX DYNAMICAL SYSTEMS","authors":"S. PRAMANICK,S. SAHA RAY","doi":"10.1142/s0218348x26501215","DOIUrl":"https://doi.org/10.1142/s0218348x26501215","url":null,"abstract":"This paper presents a novel approach for solving coupled nonlinear variable-order time-fractional sine–Gordon equations (CNVOTF-SGEs) by employing two-dimensional wavelets. When the solution of a fractional differential equation is non-smooth, weakly regular, or singular, polynomial-based methods encounter significant challenges, as polynomials are not well-suited for approximating non-smooth functions. In contrast, wavelet-based methods can approximate such functions with both accuracy and efficiency. Wavelet-based techniques often produce near-diagonal matrices, such as integral operational matrices, which significantly accelerate computations by reducing the overall computational time. Wavelets can be easily extended to two-dimensional and three-dimensional, which makes them highly effective for solving multidimensional fractional partial differential equations. The original equations are reduced to an algebraic system of equations (ASEs) by approximating the unknown functions with Jacobi and Chebyshev cardinal wavelets and by applying operational matrices together with collocation points. After solving the ASEs, we observed that the numerical results were better when using JWs compared to CCWs. Theoretical results on convergence and error estimation of the proposed method are also established. Several illustrative examples confirm the accuracy, efficiency, and applicability of the two-dimensional wavelet technique.","PeriodicalId":501262,"journal":{"name":"Fractals","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148895876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0