Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System by Xianchen Wang, Zhen Wang, Shihong Dang

“…Fractal and Fractional…”
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Beyond Chaos in Fractional-Order Systems: Keen Insight in the Dynamic Effects by José Luis Echenausía-Monroy, Luis Alberto Quezada-Tellez, Hector Eduardo Gilardi-Velázquez, Omar Fernando Ruíz-Martínez, María del Carmen Heras-Sánchez, Jose E. Lozano-Rizk, José Ricardo Cuesta-García, Luis Alejandro Márquez-Martínez, Raúl Rivera-Rodríguez, Jonatan Pena Ramirez, Joaquín Álvarez

“…Fractal and Fractional…”
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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, Wafa Khalaf Alqurashi

“…Fractal and Fractional…”
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Modeling Urban Growth and Form with Spatial Entropy by Yanguang Chen

“…Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. …”
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Rock Mechanical Property Influenced by Inhomogeneity by Yunliang Tan, Dongmei Huang, Ze Zhang

“…Different rocks behave in different fractal dimension variation patterns with the scanned magnification, so it is conditional to adopt fractal dimension to describe rock material. …”
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MODEL OF NORMAL CONTACT STIFFNESS AND DAMPING OF JOINT SURFACES CONSIDERING FRICTION AND ASPERITY INTERACTION (MT) by ZHAO HaiLu, ZHANG XueLiang, XU YongTai

“…Based on the three-dimensional fractal theory, a fractal model of normal contact stiffness and contact damping of joint surfaces considering simultaneously the influence of the friction and the asperity interaction was established. …”
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Heterogeneity and permeability estimation of pore-throat structure at different scales in deep tight sandstone reservoirs: A case study of Paleogene Hetaoyuan Formation in Anpeng a... by Yan Zhu, Yunfei Yang, Yuheng Zhang, Lin Liu, Hengquan Li, Qin Sang

“…The turning point radius of fractal curve and the comprehensive fractal dimension can be used as good indicators for permeability estimation.…”
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Aggregation Behavior of Some Asymmetric Porphyrins versus Basic Biological Tests Response by Radu Socoteanu, Mihai Anastasescu, Anabela Oliveira, Gianina Dobrescu, Rica Boscencu, Carolina Constantin

“…The correlation function method provides fractal dimension only for short scale range; results indicate that only few images have fractal properties for short ranges; for the rest of them, no fractal dimension was found using the correlation function method. …”
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The Promotion Effect of Computer-Aided Technology Combined with RBF Neural Network Algorithm on Art Design by Chunliang Pan, Yuning Pan

“…In order to improve the effect of fractal art pattern design, this study combines RBF neural network algorithm to design and evaluate CAD fractal art pattern to improve the effect of fractal art pattern design. …”
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Numerical Simulation of the Nonlinear Flow Properties in Self-Affine Aperture-Based Fractures by Xin Zhou, Jianlong Sheng, Ruili Lu, Zuyang Ye, Wang Luo

“…In order to study the effect of fracture geometry on the nonlinear flow properties in aperture-based fractures, a fractal model based on the self-affinity is proposed to characterize the three-dimensional geometry of rough-walled fractures. …”
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RESPONSE ANALYSIS OF MODAL COUPLING SYSTEM CAUSED BY ROUGH MICRO SURFACE by XIA BingXin, LI JiPing, YU LianZhou, PAN WuJiu

“…Theoretical and experimental studies have found that both fractal dimension D and fractal roughness G have an important influence on the braking stability of the system. …”
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4D Mapping of the Fracture Evolution in a Printed Gypsum-Like Core by Using X-Ray CT Scanning by Huabo Liu, Fanjing Meng, Shaozhen Hua

“…Moreover, the common approach to obtain the 3D fractal dimension of a self-similar fractal object by adding one to its corresponding 2D fractal dimension is found to be inappropriate.…”
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Assessing the global dynamics of Nipah infection under vaccination and treatment: A novel computational modeling approach. by Fang Yu, Muhammad Younas Khan, Muhammad Bilal Riaz, Saif Ullah, Muhammad Farooq

“…In biology and life sciences, fractal theory and fractional calculus have significant applications in simulating and understanding complex problems. …”
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Construction of water injection seepage model for coal body and microscopic dominant influence law by Enmao WANG, Gang WANG, Shuliang XIE, Hongzhao WEI, Jing FENG, Handan LIANG

“…The main conclusions were as follows: (1) A percolation model was established, incorporating factors such as coal body strength coefficient, tortuosity fractal dimension, effective porosity, volume fractal dimension, and pore throat radius. …”
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Applications of Magnetohydrodynamic Couple Stress Fluid Flow between Two Parallel Plates with Three Different Kernels by Imran Siddique, Ali Akgül, Hafte Amsalu Kahsay, Teklay Hailay Tsegay, Kahsay Godifey Wubneh

“…In this paper, we investigate the implementations of newly introduced nonlocal differential operators as convolution of power law, exponential decay law, and the generalized Mittag-Leffler law with fractal derivative in fluid dynamics. The new operators are referred as fractal-fractional differential operators. …”
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Correlations between Geometric Properties and Permeability of 2D Fracture Networks by Xiaolin Wang, Liyuan Yu, Hanqing Yang

“…The equivalent permeability of a fracture network increases with the increment of fracture density and/or fractal dimensions proportionally.…”
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Microarchitecture Parameters Describe Bone Structure and Its Strength Better Than BMD by Tomasz Topoliński, Adam Mazurkiewicz, Stanislaw Jung, Artur Cichański, Krzysztof Nowicki

“…The aim of this study was to find out if the values of volume, fractal dimension, and bone mineral density are correlated with bone strength. …”
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Convergence Region of Newton Iterative Power Flow Method: Numerical Studies by Jiao-Jiao Deng, Hsiao-Dong Chiang

“…Our numerical studies confirm that the convergence region of NR method has a fractal boundary and find that this fractal boundary of convergence regions persists under different loading conditions. …”
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Experimental Study on SHPB Dynamic Mechanical Response in Different Damage Zones of Rock under Blast Load by Wenda Tang, Yuanyuan You, Feng Hu, Yuanyuan Bian, Chenglong Xiao, Yijun Zhu

“…The evolution law of fractal dimension shows that with increasing distance from the core to the blast hole, the fractal dimension of the specimen after failure increases. …”
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Effect of Surface Morphology on Dynamic Characteristics of Cam-Follower Oblique Impact System by Wangqun Deng, Haibo Feng, Jianjun Wang, Yongfeng Yang

“…The effects of the fractal characteristics on the dynamic characteristics of the oblique impact system are studied via considering the normal contact stiffness with fractal dimension parameter of the microstructure of the interface in this paper. …”
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