You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.

Search for Articles:

Title / Keyword

Author / Affiliation / Email

Journal

Article Type

Advanced Search

Section

Special Issue

Volume

Issue

Number

Page

Logical OperatorOperator

Search Text

Search Type

$fractalfract-logo$

Submit to Fractal Fract Review for Fractal Fract

Journal Menu

Journal Browser

► Journal Browser

Most Cited & Viewed

Most Cited & Viewed Papers

Most Cited Papers
Most Viewed Papers
Most Downloaded Papers

Citations	Article
227	Overcoming Nonlinear Dynamics in Diabetic Retinopathy Classification: A Robust AI-Based Model with Chaotic Swarm Intelligence Optimization and Recurrent Long Short-Term Memory by Yusuf Bahri Özçelik and Aytaç Altan
164	Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption by Wei Feng, Quanwen Wang, Hui Liu, Yu Ren, Junhao Zhang, Shubo Zhang, Kun Qian and Heping Wen
100	Hydration and Fractal Analysis on Low-Heat Portland Cement Pastes Using Thermodynamics-Based Methods by Yifan Zhou, Wenwei Li, Yuxiang Peng, Shengwen Tang, Lei Wang, Yan Shi, Yang Li, Yang Wang, Zhicheng Geng and Kai Wu
66	An Improved Marine Predators Algorithm-Tuned Fractional-Order PID Controller for Automatic Voltage Regulator System by Mohd Zaidi Mohd Tumari, Mohd Ashraf Ahmad, Mohd Helmi Suid and Mok Ren Hao
63	Integrating Fractional-Order Hopfield Neural Network with Differentiated Encryption: Achieving High-Performance Privacy Protection for Medical Images by Wei Feng, Keyuan Zhang, Jing Zhang, Xiangyu Zhao, Yao Chen, Bo Cai, Zhengguo Zhu, Heping Wen and Conghuan Ye
59	Dynamic Analysis and Implementation of FPGA for a New 4D Fractional-Order Memristive Hopfield Neural Network by Fei Yu, Shankou Zhang, Dan Su, Yiya Wu, Yumba Musoya Gracia and Huige Yin
58	Chaotic Pattern and Solitary Solutions for the (21)-Dimensional Beta-Fractional Double-Chain DNA System by Tianyong Han, Kun Zhang, Yueyong Jiang and Hadi Rezazadeh
57	Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks by Majid Roohi, Saeed Mirzajani, Ahmad Reza Haghighi and Andreas Basse-O’Connor
54	Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control by Majid Roohi, Chongqi Zhang, Mostafa Taheri and Andreas Basse-O’Connor
50	Applications of Fractional-Order Calculus in Robotics by Abhaya Pal Singh and Kishore Bingi

Citations	Article
63	Integrating Fractional-Order Hopfield Neural Network with Differentiated Encryption: Achieving High-Performance Privacy Protection for Medical Images by Wei Feng, Keyuan Zhang, Jing Zhang, Xiangyu Zhao, Yao Chen, Bo Cai, Zhengguo Zhu, Heping Wen and Conghuan Ye
59	Dynamic Analysis and Implementation of FPGA for a New 4D Fractional-Order Memristive Hopfield Neural Network by Fei Yu, Shankou Zhang, Dan Su, Yiya Wu, Yumba Musoya Gracia and Huige Yin
58	Chaotic Pattern and Solitary Solutions for the (21)-Dimensional Beta-Fractional Double-Chain DNA System by Tianyong Han, Kun Zhang, Yueyong Jiang and Hadi Rezazadeh
57	Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks by Majid Roohi, Saeed Mirzajani, Ahmad Reza Haghighi and Andreas Basse-O’Connor
50	Applications of Fractional-Order Calculus in Robotics by Abhaya Pal Singh and Kishore Bingi
42	Fractals of Interpolative Kannan Mappings by Xiangting Shi, Umar Ishtiaq, Muhammad Din and Mohammad Akram
39	A New Approach Based on Metaheuristic Optimization Using Chaotic Functional Connectivity Matrices and Fractal Dimension Analysis for AI-Driven Detection of Orthodontic Growth and Development Stage by Orhan Cicek, Yusuf Bahri Özçelik and Aytaç Altan
36	Consensus of T-S Fuzzy Fractional-Order, Singular Perturbation, Multi-Agent Systems by Xiyi Wang, Xuefeng Zhang, Witold Pedrycz, Shuang-Hua Yang and Driss Boutat
36	The Use of Artificial Intelligence in Data Analysis with Error Recognitions in Liver Transplantation in HIV-AIDS Patients Using Modified ABC Fractional Order Operators by Hasib Khan, Jehad Alzabut, D. K. Almutairi and Wafa Khalaf Alqurashi
36	Dynamic Analysis and FPGA Implementation of a Fractional-Order Memristive Hopfield Neural Network with Hidden Chaotic Dual-Wing Attractors by Shaoqi He, Fei Yu, Rongyao Guo, Mingfang Zheng, Tinghui Tang, Jie Jin and Chunhua Wang

Citations	Article
36	Dynamic Analysis and FPGA Implementation of a Fractional-Order Memristive Hopfield Neural Network with Hidden Chaotic Dual-Wing Attractors by Shaoqi He, Fei Yu, Rongyao Guo, Mingfang Zheng, Tinghui Tang, Jie Jin and Chunhua Wang
35	Structural Performance Warning Based on Computer Intelligent Monitoring and Fractional-Order Multi-Rate Kalman Fusion Method by Yan Wang, Yan Shi, Taoyuan Yang, Weinan Wang, Zhongmiao Sun and Yuqi Zhang
34	State-Dependent Variable Fractional-Order Hyperchaotic Dynamics in a Coupled Quadratic Map: A Novel System for High-Performance Image Protection by Wei Feng, Zixian Tang, Xiangyu Zhao, Zhentao Qin, Yao Chen, Bo Cai, Zhengguo Zhu, Heping Wen and Conghuan Ye
32	Automatic Picking Method for the First Arrival Time of Microseismic Signals Based on Fractal Theory and Feature Fusion by Huicong Xu, Kai Li, Pengfei Shan, Xuefei Wu, Shuai Zhang, Zeyang Wang, Chenguang Liu, Zhongming Yan, Liang Wu and Huachuan Wang
20	Multifractal Characterization of Heterogeneous Pore Water Redistribution and Its Influence on Permeability During Depletion: Insights from Centrifugal NMR Analysis by Fangkai Quan, Wei Lu, Yu Song, Wenbo Sheng, Zhengyuan Qin and Huogen Luo
17	A Novel Softsign Fractional-Order Controller Optimized by an Intelligent Nature-Inspired Algorithm for Magnetic Levitation Control by Davut Izci, Serdar Ekinci, Mohd Zaidi Mohd Tumari and Mohd Ashraf Ahmad
15	A Fractional Derivative Insight into Full-Stage Creep Behavior in Deep Coal by Shuai Yang, Hongchen Song, Hongwei Zhou, Senlin Xie, Lei Zhang and Wentao Zhou
14	A Fractional-Order SSIM-Based Gaussian Loss with Long-Range Memory for Dense VSLAM by Junyang Zhao, Huixin Zhu, Zhili Zhang, Mingtao Feng, Han Yu and Yuxuan Li
13	A Kangaroo Escape Optimizer-Enabled Fractional-Order PID Controller for Enhancing Dynamic Stability in Multi-Area Power Systems by Sulaiman Z. Almutairi and Abdullah M. Shaheen
13	Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method by Sarfaraz Ahmed, Ibtisam Aldawish, Syed T. R. Rizvi and Aly R. Seadawy

Citations	Article
35	Structural Performance Warning Based on Computer Intelligent Monitoring and Fractional-Order Multi-Rate Kalman Fusion Method by Yan Wang, Yan Shi, Taoyuan Yang, Weinan Wang, Zhongmiao Sun and Yuqi Zhang
11	New Fixed-Time Synchronization Criteria for Fractional-Order Fuzzy Cellular Neural Networks with Bounded Uncertainties and Transmission Delays via Multi-Module Control Schemes by Hongguang Fan, Hui Wen, Kaibo Shi and Jianying Xiao
7	Existence of Heteroclinic Orbits in Fractional-Order and Integer-Order Coupled Lorenz Systems by Guiyao Ke, Jun Pan, Feiyu Hu and Haijun Wang
6	Influence of Initial Stress on Wave Propagation in Microelongated Thermo-Elastic Media Under the Refined Fractional Dual Phase Lag Model by Mohamed F. Ismail, Hamdy M. Ahmed, Taha Radwan, Soliman Alkhatib, M. Elsaid Ramadan and Eslam Nabil Shawki El-Ganzoury
6	Characterization and Analysis of Hybrid Fractal Antennas for Multiband Communication and Radar Applications by Abdelbasset Azzouz, Rachid Bouhmidi, Mehr E. Munir, Moustafa M. Nasralla and Mohammed Chetioui
6	A Fractional Hybrid Strategy for Reliable and Cost-Optimal Economic Dispatch in Wind-Integrated Power Systems by Abdul Wadood, Babar Sattar Khan, Bakht Muhammad Khan, Herie Park and Byung O. Kang
6	Exploring Fixed-Time Synchronization of Fractional-Order Fuzzy Cellular Neural Networks with Information Interactions and Time-Varying Delays via Adaptive Multi-Module Control by Hongguang Fan, Kaibo Shi, Anran Zhou, Fei Meng and Liang Jiang
4	Optimal Fractional Order PID Controller Design for Hydraulic Turbines Using a Multi-Objective Imperialist Competitive Algorithm by Mohamed Nejlaoui, Abdullah Alghafis and Nasser Ayidh Alqahtani
4	Multi-Objective Optimization and Load-Flow Analysis in Complex Power Distribution Networks by Tariq Ali, Muhammad Ayaz, Husam S. Samkari, Mohammad Hijji, Mohammed F. Allehyani and El-Hadi M. Aggoune
4	A Hybrid Neural Network Approach to Controllability in Caputo Fractional Neutral Integro-Differential Systems for Cryptocurrency Forecasting by Prabakaran Raghavendran and Yamini Parthiban

Citations	Article
227	Overcoming Nonlinear Dynamics in Diabetic Retinopathy Classification: A Robust AI-Based Model with Chaotic Swarm Intelligence Optimization and Recurrent Long Short-Term Memory by Yusuf Bahri Özçelik and Aytaç Altan
200	Study on Date–Jimbo–Kashiwara–Miwa Equation with Conformable Derivative Dependent on Time Parameter to Find the Exact Dynamic Wave Solutions by Md Ashik Iqbal, Ye Wang, Md Mamun Miah and Mohamed S. Osman
197	Forecasting Cryptocurrency Prices Using LSTM, GRU, and Bi-Directional LSTM: A Deep Learning Approach by Phumudzo Lloyd Seabe, Claude Rodrigue Bambe Moutsinga and Edson Pindza
191	Structure, Fractality, Mechanics and Durability of Calcium Silicate Hydrates by Shengwen Tang, Yang Wang, Zhicheng Geng, Xiaofei Xu, Wenzhi Yu, Hubao A and Jingtao Chen
164	Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption by Wei Feng, Quanwen Wang, Hui Liu, Yu Ren, Junhao Zhang, Shubo Zhang, Kun Qian and Heping Wen
146	Fractal Analysis on Pore Structure and Hydration of Magnesium Oxysulfate Cements by First Principle, Thermodynamic and Microstructure-Based Methods by Jiasheng Huang, Wenwei Li, Desheng Huang, Lei Wang, E Chen, Chengyou Wu, Baoshan Wang, Hongyang Deng, Shengwen Tang, Yan Shi and Yang Li
144	Investigation and Application of Fractal Theory in Cement-Based Materials: A Review by Lei Wang, Xiaoman Zeng, Huamei Yang, Xingdong Lv, Fanxing Guo, Yan Shi and Asad Hanif
140	Homotopy Perturbation Method for the Fractal Toda Oscillator by Ji-Huan He, Yusry O. El-Dib and Amal A. Mady
128	Stability Analysis and Numerical Computation of the Fractional Predator–Prey Model with the Harvesting Rate by Mehmet Yavuz and Ndolane Sene
121	Multiple-Layer Image Encryption Utilizing Fractional-Order Chen Hyperchaotic Map and Cryptographically Secure PRNGs by Wassim Alexan, Nader Alexan and Mohamed Gabr

More Articles...

Views	Article
12735	An Overview of Mathematical Modelling in Cancer Research: Fractional Calculus as Modelling Tool by Lourenço Côrte Vieira, Rafael S. Costa and Duarte Valério
10319	Some Insights into the Sierpiński Triangle Paradox by Miguel-Ángel Martínez-Cruz, Julián Patiño-Ortiz, Miguel Patiño-Ortiz and Alexander S. Balankin
10296	Hydration and Fractal Analysis on Low-Heat Portland Cement Pastes Using Thermodynamics-Based Methods by Yifan Zhou, Wenwei Li, Yuxiang Peng, Shengwen Tang, Lei Wang, Yan Shi, Yang Li, Yang Wang, Zhicheng Geng and Kai Wu
8890	Approximation of Caputo Fractional Derivative and Numerical Solutions of Fractional Differential Equations by Yuri Dimitrov, Slavi Georgiev and Venelin Todorov
8710	Proposal for Use of the Fractional Derivative of Radial Functions in Interpolation Problems by Anthony Torres-Hernandez, Fernando Brambila-Paz and Rafael Ramirez-Melendez
8085	Day of the Week Effect on the World Exchange Rates through Fractal Analysis by Werner Kristjanpoller and Benjamin Miranda Tabak
7980	Review of the Fractional Black-Scholes Equations and Their Solution Techniques by Hongmei Zhang, Mengchen Zhang, Fawang Liu and Ming Shen
7143	*The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems* by Patricio Venegas-Aravena and Enrique G. Cordaro
7018	Chance or Chaos? Fractal Geometry Aimed to Inspect the Nature of Bitcoin by Esther Cabezas-Rivas, Felipe Sánchez-Coll and Isaac Tormo-Xaixo
6995	A Brief Survey of Paradigmatic Fractals from a Topological Perspective by Julián Patiño Ortiz, Miguel Patiño Ortiz, Miguel-Ángel Martínez-Cruz and Alexander S. Balankin

Views	Article
10319	Some Insights into the Sierpiński Triangle Paradox by Miguel-Ángel Martínez-Cruz, Julián Patiño-Ortiz, Miguel Patiño-Ortiz and Alexander S. Balankin
6421	Inner Multifractal Dynamics in the Jumps of Cryptocurrency and Forex Markets by Haider Ali, Muhammad Aftab, Faheem Aslam and Paulo Ferreira
6047	Proposal for the Application of Fractional Operators in Polynomial Regression Models to Enhance the Determination Coefficient R² on Unseen Data by Anthony Torres-Hernandez, Rafael Ramirez-Melendez and Fernando Brambila-Paz
5886	Fractal Dimensional Analysis of Building Facades: The Case of Office Buildings in Erbil City by Lana Abubakr Ali and Faris Ali Mustafa
5877	Uncertainty-Aware Self-Attention Model for Time Series Prediction with Missing Values by Jiabao Li, Chengjun Wang, Wenhang Su, Dongdong Ye and Ziyang Wang
5815	Fractal Properties of the Cosmic Web by Jaan Einasto
5485	A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry by Romolo Marcelli
5275	Graph-Based Stock Volatility Forecasting with Effective Transfer Entropy and Hurst-Based Regime Adaptation by Sangheon Lee and Poongjin Cho
5076	Time-Varying Market Efficiency: A Focus on Crude Oil and Commodity Dynamics by Young-Sung Kim, Do-Hyeon Kim, Dong-Jun Kim and Sun-Yong Choi
4841	Hover Flight Improvement of a Quadrotor Unmanned Aerial Vehicle Using PID Controllers with an Integral Effect Based on the Riemann–Liouville Fractional-Order Operator: A Deterministic Approach by Gustavo Delgado-Reyes, Jorge Salvador Valdez-Martínez, Pedro Guevara-López and Miguel Angel Hernández-Pérez

Views	Article
5815	Fractal Properties of the Cosmic Web by Jaan Einasto
5485	A Multidisciplinary Approach to Triangular Shapes: Philosophy, Art, Mathematical Properties, and Application Purposes for High-Frequency Signal Processing Using Sierpiński Geometry by Romolo Marcelli
3958	Bidirectional Mamba-Enhanced 3D Human Pose Estimation for Accurate Clinical Gait Analysis by Chengjun Wang, Wenhang Su, Jiabao Li and Jiahang Xu
3728	Stylized Facts of High-Frequency Bitcoin Time Series by Yaoyue Tang, Karina Arias-Calluari, Morteza Nattagh Najafi, Michael S. Harré and Fernando Alonso-Marroquin
3576	Fractal Technology for Sustainable Growth in the AI Era: Fractal Principles for Industry 5.0 by Young Chan Ko, Soon Wan Kweon, Byoung Geun Moon, Jong-Moon Park and Hyoung Jin Kim
3265	Normalized Ground States for Mixed Fractional Schrödinger Equations with Combined Local and Nonlocal Nonlinearities by Jie Yang and Haibo Chen
3245	Artificial Intelligence-Based Plant Disease Classification in Low-Light Environments by Hafiz Ali Hamza Gondal, Seong In Jeong, Won Ho Jang, Jun Seo Kim, Rehan Akram, Muhammad Irfan, Muhammad Hamza Tariq and Kang Ryoung Park
3184	Systemic Risk Contagion in China’s Financial–Real Estate Network: Modeling and Forecasting via Fractional-Order PDEs by Weiye Sun, Yulian An and Yijin Gao
3149	When RNN Meets CNN and ViT: The Development of a Hybrid U-Net for Medical Image Segmentation by Ziru Wang and Ziyang Wang
2853	From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding by Mauricio J. D. Martins

Views	Article
1662	From Mathematics to Art: A Petri Net Representation of the Fibonacci Sequence and Its Fractal Geometry by David Mailland and Iwona Grobelna
1624	HR-UMamba++: A High-Resolution Multi-Directional Mamba Framework for Coronary Artery Segmentation in X-Ray Coronary Angiography by Xiuhan Zhang, Peng Lu, Zongsheng Zheng and Wenhui Li
1592	Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach by Wenhao Zhang, Zhenpeng Tang, Xiaowen Zhuang, Yi Cai and Baihua Dong
1459	Numerical Fractional Calculus Framework for Nonlocal Euler–Bernoulli Beam Deflection Analysis by Amirhosein Bahreini, Ali Asgari, Reza Taghipour, Hossein Jafari and Habib Akbarzadeh Bengar
1345	Fractal Duffing Oscillators with Two Degrees of Freedom and Cubic–Quintic Nonlinear Stiffness by Guozhong Xiu, Jihuan He, Yusry O. El-Dib and Haifa A. Alyousef
1329	Characterization and Analysis of Hybrid Fractal Antennas for Multiband Communication and Radar Applications by Abdelbasset Azzouz, Rachid Bouhmidi, Mehr E. Munir, Moustafa M. Nasralla and Mohammed Chetioui
1297	Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods, and Applications by Wenying Feng
1150	Cascaded Optimized Fractional Controller for Green Hydrogen-Based Microgrids with Mitigating False Data Injection Attacks by Nadia A. Nagem, Mokhtar Aly, Emad A. Mohamed, Aisha F. Fareed, Dokhyl M. Alqahtani and Wessam A. Hafez
1149	Estimation of Fractal Dimension and Super-Resolution Reconstruction for Person Re-Identification in Images from Infrared Surveillance Camera by Seung Yong Jung, Dong Chan Lee, Min Su Jeong, Seong In Jeong, Hyun Woo Song, Ho Won Lee and Kang Ryoung Park
1125	Optimization Design Method for Full-Bridge LLC Resonant Converter Based on Fractional-Order Characteristics of Resonant Tank by Xiaoquan Zhu, Chentao Ma and Haochi He

Views	Article
41471	Forecasting Cryptocurrency Prices Using LSTM, GRU, and Bi-Directional LSTM: A Deep Learning Approach by Phumudzo Lloyd Seabe, Claude Rodrigue Bambe Moutsinga and Edson Pindza
18390	Fractal Antennas: An Historical Perspective by Jaume Anguera, Aurora Andújar, Jeevani Jayasinghe, V. V. S. S. Sameer Chakravarthy, P. S. R. Chowdary, Joan L. Pijoan, Tanweer Ali and Carlo Cattani
18077	Fractal, Scale Free Electromagnetic Resonance of a Single Brain Extracted Microtubule Nanowire, a Single Tubulin Protein and a Single Neuron by Komal Saxena, Pushpendra Singh, Pathik Sahoo, Satyajit Sahu, Subrata Ghosh, Kanad Ray, Daisuke Fujita and Anirban Bandyopadhyay
16479	Structure, Fractality, Mechanics and Durability of Calcium Silicate Hydrates by Shengwen Tang, Yang Wang, Zhicheng Geng, Xiaofei Xu, Wenzhi Yu, Hubao A and Jingtao Chen
16081	Utilizing Fractals for Modeling and 3D Printing of Porous Structures by AMM Sharif Ullah, Doriana Marilena D’Addona, Yusuke Seto, Shota Yonehara and Akihiko Kubo
14955	Fractals: An Eclectic Survey, Part-I by Akhlaq Husain, Manikyala Navaneeth Nanda, Movva Sitaram Chowdary and Mohammad Sajid
13521	The Mathematics of ‘Natural Beauty’ in the Architecture of Andrea Palladio and Le Corbusier: An Analysis of Colin Rowe’s Theory of Formal Complexity Using Fractal Dimensions by Michael J. Dawes, Michael J. Ostwald and Ju Hyun Lee
12752	Comparing Market Efficiency in Developed, Emerging, and Frontier Equity Markets: A Multifractal Detrended Fluctuation Analysis by Min-Jae Lee and Sun-Yong Choi
12735	An Overview of Mathematical Modelling in Cancer Research: Fractional Calculus as Modelling Tool by Lourenço Côrte Vieira, Rafael S. Costa and Duarte Valério
11784	*Examining the Position of Wright’s Fallingwater* in the Context of His Larger Body of Work: An Analysis Using Fractal Dimensions by Josephine Vaughan and Michael J. Ostwald**

More Articles...

Downloads	Article
6429	Models for Simulation of Fractal-like Particle Clusters with Prescribed Fractal Dimension by Oleksandr Tomchuk
2348	Overcoming Nonlinear Dynamics in Diabetic Retinopathy Classification: A Robust AI-Based Model with Chaotic Swarm Intelligence Optimization and Recurrent Long Short-Term Memory by Yusuf Bahri Özçelik and Aytaç Altan
2216	Metaheuristic-Based Algorithms for Optimizing Fractional-Order Controllers—A Recent, Systematic, and Comprehensive Review by Ahmed M. Nassef, Mohammad Ali Abdelkareem, Hussein M. Maghrabie and Ahmad Baroutaji
1989	Hydration and Fractal Analysis on Low-Heat Portland Cement Pastes Using Thermodynamics-Based Methods by Yifan Zhou, Wenwei Li, Yuxiang Peng, Shengwen Tang, Lei Wang, Yan Shi, Yang Li, Yang Wang, Zhicheng Geng and Kai Wu
1951	Review of the Fractional Black-Scholes Equations and Their Solution Techniques by Hongmei Zhang, Mengchen Zhang, Fawang Liu and Ming Shen
1866	Novel Meta-Fractal Wearable Sensors and Antennas for Medical, Communication, 5G, and IoT Applications by Albert Sabban
1820	An Overview of Mathematical Modelling in Cancer Research: Fractional Calculus as Modelling Tool by Lourenço Côrte Vieira, Rafael S. Costa and Duarte Valério
1736	Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption by Wei Feng, Quanwen Wang, Hui Liu, Yu Ren, Junhao Zhang, Shubo Zhang, Kun Qian and Heping Wen
1710	Application of Tilt Integral Derivative for Efficient Speed Control and Operation of BLDC Motor Drive for Electric Vehicles by Khairy Sayed, Hebatallah H. El-Zohri, Adel Ahmed and Mohamed Khamies
1569	*The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems* by Patricio Venegas-Aravena and Enrique G. Cordaro

Downloads	Article
1203	Damage Law and Reasonable Width of Coal Pillar under Gully Area: Linking Fractal Characteristics of Coal Pillar Fractures to Their Stability by Zhaopeng Wu, Yunpei Liang, Kaijun Miao, Qigang Li, Sichen Liu, Qican Ran, Wanjie Sun, Hualong Yin and Yun Ma
1176	Predicting the Deformation of a Slope Using a Random Coefficient Panel Data Model by Zhenxia Yuan, Yadong Bian, Weijian Liu, Fuzhou Qi, Haohao Ma, Sen Zheng and Zhenzhu Meng
1060	Fractal Dimension-Based Multi-Focus Image Fusion via Coupled Neural P Systems in NSCT Domain by Liangliang Li, Xiaobin Zhao, Huayi Hou, Xueyu Zhang, Ming Lv, Zhenhong Jia and Hongbing Ma
1056	Fractional-Order Modeling and Identification for an SCR Denitrification Process by Wei Ai, Xinlei Lin, Ying Luo and Xiaowei Wang
1051	Fractal Dimensional Analysis of Building Facades: The Case of Office Buildings in Erbil City by Lana Abubakr Ali and Faris Ali Mustafa
1051	RGB-D Camera and Fractal-Geometry-Based Maximum Diameter Estimation Method of Apples for Robot Intelligent Selective Graded Harvesting by Bin Yan and Xiameng Li
1013	High-Order Numerical Approximation for 2D Time-Fractional Advection–Diffusion Equation under Caputo Derivative by Xindong Zhang, Yan Chen and Leilei Wei
1012	Robust Design of Two-Level Non-Integer SMC Based on Deep Soft Actor-Critic for Synchronization of Chaotic Fractional Order Memristive Neural Networks by Majid Roohi, Saeed Mirzajani, Ahmad Reza Haghighi and Andreas Basse-O’Connor
996	A Computational Method for Solving Nonlinear Fractional Integral Equations by Rajaa T. Matoog, Amr M. S. Mahdy, Mohamed A. Abdou and Doaa Sh. Mohamed
990	Novel Fractional Order Differential and Integral Models for Wind Turbine Power–Velocity Characteristics by Ahmed G. Mahmoud, Mohamed A. El-Beltagy and Ahmed M. Zobaa

Downloads	Article
965	Robust Generalized Transient-Extracting Transform for Time–Frequency Feature Extraction by Junbo Long, Dongyun Luo, Daifeng Zha, Honglian Wu, Tong Shu and Hongshe Fan
725	Dynamic Analysis and FPGA Implementation of a Fractional-Order Memristive Hopfield Neural Network with Hidden Chaotic Dual-Wing Attractors by Shaoqi He, Fei Yu, Rongyao Guo, Mingfang Zheng, Tinghui Tang, Jie Jin and Chunhua Wang
717	Fractal Properties of the Cosmic Web by Jaan Einasto
687	Hardware-in-the-Loop Experimental Validation of a Fault-Tolerant Control System for Quadcopter UAV Motor Faults by Muhammad Abdullah, Adil Zulfiqar, Muhammad Zeeshan Babar, Jamal Hussain Arman, Ghulam Hafeez, Ahmed S. Alsafran and Muhyaddin Rawa
684	Bidirectional Mamba-Enhanced 3D Human Pose Estimation for Accurate Clinical Gait Analysis by Chengjun Wang, Wenhang Su, Jiabao Li and Jiahang Xu
680	Chaotic Dynamics and Fractal Geometry in Ring Lattice Systems of Nonchaotic Rulkov Neurons by Brandon B. Le
676	Mechanical Properties and Energy Absorption Characteristics of the Fractal Structure of the Royal Water Lily Leaf Under Quasi-Static Axial Loading by Zhanhong Guo, Zhaoyang Wang, Weiguang Fan, Hailong Yu and Meng Zou
660	Multifractal Characterization of Marine Shale Pore Structure Alteration Induced by Supercritical CO₂–Water–Rock Interaction by Haonan Wei, Yi Du, Changqing Fu, Gaoqiang Fu, Yingfang Zhou, Jinfeng Ma, Zhenliang Wang, Zhejun Pan and Wei Gao
657	Exact Solitary Wave Solutions and Sensitivity Analysis of the Fractional (3+1)D KdV–ZK Equation by Asif Khan, Fehaid Salem Alshammari, Sadia Yasin and Beenish
641	Rolling Bearing Fault Diagnosis Based on Fractional Constant Q Non-Stationary Gabor Transform and VMamba-Conv by Fengyun Xie, Chengjie Song, Yang Wang, Minghua Song, Shengtong Zhou and Yuanwei Xie

Downloads	Article
965	Robust Generalized Transient-Extracting Transform for Time–Frequency Feature Extraction by Junbo Long, Dongyun Luo, Daifeng Zha, Honglian Wu, Tong Shu and Hongshe Fan
319	A 5D Fractional-Order Memristive Neural Network for Satellite Image Encryption Using Dynamic DNA Encoding and Bidirectional Diffusion by Jinghui Ding, Yanping Zhu, Weiquan Yin, Dazhe He, Fayu Wan and Gangyi Tu
305	Optimal Fractional Order PID Controller Design for Hydraulic Turbines Using a Multi-Objective Imperialist Competitive Algorithm by Mohamed Nejlaoui, Abdullah Alghafis and Nasser Ayidh Alqahtani
287	A Fast L2-1_σ Finite Element Method for Time Fractional Keller–Segel Equations with Weakly Singular Solutions by Qingfeng Li, Jia Xie and Shirong Chen
276	Cascaded Optimized Fractional Controller for Green Hydrogen-Based Microgrids with Mitigating False Data Injection Attacks by Nadia A. Nagem, Mokhtar Aly, Emad A. Mohamed, Aisha F. Fareed, Dokhyl M. Alqahtani and Wessam A. Hafez
267	Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods, and Applications by Wenying Feng
263	On the Tantawy Technique for Analyzing Fractional Kuramoto–Sivashinsky-Type Equations and Modeling Shock Waves in Plasmas and Fluids—Part (I), Planar Case by Samir A. El-Tantawy, Alvaro H. Salas, Wedad Albalawi, Rania A. Alharbey and Ashwag A. Alharby
259	HR-UMamba++: A High-Resolution Multi-Directional Mamba Framework for Coronary Artery Segmentation in X-Ray Coronary Angiography by Xiuhan Zhang, Peng Lu, Zongsheng Zheng and Wenhui Li
258	Temperature-Dependent Pore Size Redistribution and Fractal Complexity in Low-Maturity Shale: Implications for In Situ Conversion by Qiansong Guo, Xianda Sun, Yuchen Wang, Chengwu Xu, Wei Li and Changxin He
257	A Comprehensive Analysis of Proportional Caputo-Hybrid Fractional Inequalities and Numerical Verification via Artificial Neural Networks by Ayed R. A. Alanzi, Mariem Al-Hazmy, Raouf Fakhfakh, Wedad Saleh, Abdellatif Ben Makhlouf and Abdelghani Lakhdari

Downloads	Article
7995	Forecasting Cryptocurrency Prices Using LSTM, GRU, and Bi-Directional LSTM: A Deep Learning Approach by Phumudzo Lloyd Seabe, Claude Rodrigue Bambe Moutsinga and Edson Pindza
6520	Towards a Generalized Beer-Lambert Law by Giampietro Casasanta and Roberto Garra
6429	Models for Simulation of Fractal-like Particle Clusters with Prescribed Fractal Dimension by Oleksandr Tomchuk
4985	Fractional Definite Integral by Manuel Ortigueira and José Machado
4387	Some New Versions of Fractional Inequalities for Exponential Trigonometric Convex Mappings via Ordered Relation on Interval-Valued Settings by Muhammad Bilal Khan, Adriana Cătaş, Najla Aloraini and Mohamed S. Soliman
4374	Fractal Antennas: An Historical Perspective by Jaume Anguera, Aurora Andújar, Jeevani Jayasinghe, V. V. S. S. Sameer Chakravarthy, P. S. R. Chowdary, Joan L. Pijoan, Tanweer Ali and Carlo Cattani
3746	Structure, Fractality, Mechanics and Durability of Calcium Silicate Hydrates by Shengwen Tang, Yang Wang, Zhicheng Geng, Xiaofei Xu, Wenzhi Yu, Hubao A and Jingtao Chen
3654	Regularized Integral Representations of the Reciprocal Gamma Function by Dimiter Prodanov
3535	Generalized Memory: Fractional Calculus Approach by Vasily E. Tarasov
3498	Investigation on Pore Structure and Permeability of Concrete–Rock Interfacial Transition Zones Based on Fractal Theory by Juan Yue, Jinchang Sheng, Huimin Wang, Yunjin Hu, Kailai Zhang, Yulong Luo, Qing Zhou and Meili Zhan

Most Cited & Viewed Special Issues

Most Cited Special Issues
Most Viewed Special Issues

Avg. Citations	Special Issue
17.36	Advances in Fractional-Order Chaotic and Complex Systems Guest Editors Chunhua Wang , Fei Yu and Wei Yao \| Number of Papers: 11
11	Fractional Order Systems with Application to Electrical Power Engineering, 2nd Edition Guest Editors Arman Oshnoei and Mahdieh Sadat Sadabadi \| Number of Papers: 11
10.9	Analysis and Modeling of Fractional-Order Dynamical Networks Guest Editors Fei Wang and Feifei Du \| Number of Papers: 10
10.2	Fractional Order Controllers for Non-linear Systems Guest Editors Chendrayan Dineshkumar and Velusamy Vijayakumar \| Number of Papers: 10
9.23	Applications of Fractal Analysis in Underground Engineering Guest Editors Shihao Tu , Lei Zhang , Chen Wang , Cun Zhang , Defu Zhu and Kaijun Miao \| Number of Papers: 13
8.79	Fractal and Fractional in Geotechnical Engineering Guest Editors Shao-Heng He, Zhi Ding and Panpan Guo \| Number of Papers: 14
8.25	Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs Guest Editors Zine El Abiddine Fellah , Jizhen Zhang and Quanzhong Guan \| Number of Papers: 24
7.92	Modeling, Optimization, and Control of Fractional-Order Neural Networks and Nonlinear Systems Guest Editors Kaibo Shi , Zhinan Peng , Xin Wang and Xiao Cai \| Number of Papers: 13
7.5	Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering Guest Editors Alexandra M. S. F. Galhano, Sergio Adriani David and António Lopes \| Number of Papers: 12
6.64	Advances in Fractional Differential Operators and Their Applications, 2nd Edition Guest Editors Angelo B. Mingarelli , Leila Gholizadeh Zivlaei and Mohammad Dehghan \| Number of Papers: 11

More Special Issues...

Views	Special Issue
50885	Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs Guest Editors Zine El Abiddine Fellah , Jizhen Zhang and Quanzhong Guan \| Number of Papers: 24
44007	Fractional Order Controllers for Non-linear Systems Guest Editors Chendrayan Dineshkumar and Velusamy Vijayakumar \| Number of Papers: 10
37432	Fractal and Fractional in Geotechnical Engineering Guest Editors Shao-Heng He, Zhi Ding and Panpan Guo \| Number of Papers: 14
35241	Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering Guest Editors Alexandra M. S. F. Galhano, Sergio Adriani David and António Lopes \| Number of Papers: 12
34270	Modeling, Optimization, and Control of Fractional-Order Neural Networks and Nonlinear Systems Guest Editors Kaibo Shi , Zhinan Peng , Xin Wang and Xiao Cai \| Number of Papers: 13
33019	Applications of Fractional-Order Grey Models Guest Editors Shuli Yan and Lifeng Wu \| Number of Papers: 14
32707	Fractional Systems, Integrals and Derivatives: Theory and Application Guest Editors Andrey Zahariev and Hristo Kiskinov \| Number of Papers: 20
30817	Fractional Mathematical Modelling: Theory, Methods and Applications Guest Editors Faranak Rabiei, Dongwook Kim and Zeeshan Ali \| Number of Papers: 13
30058	Fractional Order Systems with Application to Electrical Power Engineering, 2nd Edition Guest Editors Arman Oshnoei and Mahdieh Sadat Sadabadi \| Number of Papers: 11
29437	Analysis and Numerical Computations of Nonlinear Fractional and Classical Differential Equations Guest Editors Xiao-Jun Yang , Wenxue Zhou , Sunil Dutt Purohit , Ali Turab and Ahmed Refaie Ali \| Number of Papers: 20

More Special Issues...

Back to TopTop