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ANISOTROPY AND SIZE EFFECT OF THE FRACTAL CHARACTERISTICS OF ROCK FRACTURE SURFACES UNDER MICROWAVE IRRADIATION: AN EXPERIMENTAL RESEARCH Fractals (IF 4.7) Pub Date : 2024-04-25 BEN-GAO YANG, JING XIE, YI-MING YANG, JUN-JUN LIU, SI-QI YE, RUI-FENG TANG, MING-ZHONG GAO
Studying the rough structure characteristics of rock fracture surfaces under microwave irradiation is of a great significance for understanding the rock-breaking mechanism. Therefore, this work takes fracture surface as the research object under three failure modes: microwave irradiation, uniaxial loading and microwave-uniaxial loading. The undulation and roughness are used to describe the morphological
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THE FRACTAL STRUCTURE OF ANALYTICAL SOLUTIONS TO FRACTIONAL RICCATI EQUATION Fractals (IF 4.7) Pub Date : 2024-04-25 ZENONAS NAVICKAS, TADAS TELKSNYS, INGA TELKSNIENE, ROMAS MARCINKEVICIUS, MINVYDAS RAGULSKIS
Analytical solutions to the fractional Riccati equation are considered in this paper. Solutions to fractional differential equations are expressed in the form of fractional power series in the Caputo algebra. It is demonstrated that solutions to higher-order Riccati fractional equations inherit some solutions from lower-order Riccati equations under special initial conditions. Such nested and fractal-like
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VARIATIONAL PERSPECTIVE TO (2+1)-DIMENSIONAL KADOMTSEV–PETVIASHVILI MODEL AND ITS FRACTAL MODEL Fractals (IF 4.7) Pub Date : 2024-04-25 KANG-LE WANG
In this work, the (2+1)-dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative
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SOME NEW TYPES OF GRONWALL-BELLMAN INEQUALITY ON FRACTAL SET Fractals (IF 4.7) Pub Date : 2024-04-20 GUOTAO WANG, RONG LIU
Gronwall–Bellman-type inequalities provide a very effective way to investigate the qualitative and quantitative properties of solutions of nonlinear integral and differential equations. In recent years, local fractional calculus has attracted the attention of many researchers. In this paper, based on the basic knowledge of local fractional calculus and the method of proving inequality on the set of
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INTELLIGENT EXTRACTION OF COMPLEXITY TYPES IN FRACTAL RESERVOIR AND ITS SIGNIFICANCE TO ESTIMATE TRANSPORT PROPERTY Fractals (IF 4.7) Pub Date : 2024-04-20 YI JIN, BEN ZHAO, YUNHANG YANG, JIABIN DONG, HUIBO SONG, YUNQING TIAN, JIENAN PAN
Fractal pore structure exists widely in natural reservoir and dominates its transport property. For that, more and more effort is devoted to investigate the control mechanism on mass transfer in such a complex and multi-scale system. Apparently, effective characterization of the fractal structure is of fundamental importance. Although the newly emerged concept of complexity assembly clarified the complexity
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BOX DIMENSION OF FRACTAL INTERPOLATION SURFACES WITH VERTICAL SCALING FUNCTION Fractals (IF 4.7) Pub Date : 2024-04-20 LAI JIANG
In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized affine fractal interpolation surfaces (FISs). By using these matrices, we establish relationships between oscillation vectors of different levels, which enables us
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ATTACK VULNERABILITY OF FRACTAL SCALE-FREE NETWORK Fractals (IF 4.7) Pub Date : 2024-04-13 FEIYAN GUO, LIN QI, YING FAN
An in-depth analysis of the attack vulnerability of fractal scale-free networks is of great significance for designing robust networks. Previous studies have mainly focused on the impact of fractal property on attack vulnerability of scale-free networks under static node attacks, while we extend the study to the cases of various types of targeted attacks, and explore the relationship between the attack
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A NEW PERSPECTIVE ON THE NONLINEAR DATE–JIMBO–KASHIWARA–MIWA EQUATION IN FRACTAL MEDIA Fractals (IF 4.7) Pub Date : 2024-04-12 JIANSHE SUN
In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered
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A FRACTAL-BASED OIL TRANSPORT MODEL WITH UNCERTAINTY REDUCTION FOR A MULTI-SCALE SHALE PORE SYSTEM Fractals (IF 4.7) Pub Date : 2024-04-10 WENHUI SONG, YUNHU LU, YIHUA GAO, BOWEN YAO, YAN JIN, MIAN CHEN
The challenges of modeling shale oil transport are numerous and include strong solid-fluid interactions, fluid rheology, the multi-scale nature of the pore structure problem, and the different pore types involved. Until now, theoretical studies have not fully considered shale oil transport mechanisms and multi-scale pore structure properties. In this study, we propose a fractal-based oil transport
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NOVEL UNIFIED STABILITY CRITERION FOR FRACTIONAL-ORDER TIME DELAY SYSTEMS WITH STRONG RESISTANCE TO FRACTIONAL ORDERS Fractals (IF 4.7) Pub Date : 2024-04-09 ZHE ZHANG, CHENGHAO XU, YAONAN WANG, JIANQIAO LUO, XU XIAO
In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic
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SOME RESULTS ON BOX DIMENSION ESTIMATION OF FRACTAL CONTINUOUS FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-04-09 HUAI YANG, LULU REN, QIAN ZHENG
In this paper, we explore upper box dimension of continuous functions on [0,1] and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed 2−υ, the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of
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A STUDY OF THE THERMAL EVOLUTION OF PERMEABILITY AND POROSITY OF POROUS ROCKS BASED ON FRACTAL GEOMETRY THEORY Fractals (IF 4.7) Pub Date : 2024-04-09 TONGJUN MIAO, AIMIN CHEN, RICHENG LIU, PENG XU, BOMING YU
The temperature effect on the permeability of porous rocks continues to be a considerable controversy in the area of reservoirs since the thermal expansion of mineral grains exhibits complicated influence on pore geometries in them. To investigate the degree of effect of pore structures on the hydro-thermal coupling process, a study of the thermal evolution of permeability and porosity of porous rocks
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FRACTAL DIMENSIONS FOR THE MIXED (κ,s)-RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF BIVARIATE FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-04-09 B. Q. WANG, W. XIAO
The research object of this paper is the mixed (κ,s)-Riemann–Liouville fractional integral of bivariate functions on rectangular regions, which is a natural generalization of the fractional integral of univariate functions. This paper first indicates that the mixed integral still maintains the validity of the classical properties, such as boundedness, continuity and bounded variation. Furthermore,
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ANALYSIS OF THE EFFECT OF VARIOUS MENTAL TASKS ON THE EEG SIGNALS’ COMPLEXITY Fractals (IF 4.7) Pub Date : 2024-04-09 NAJMEH PAKNIYAT, ONDREJ KREJCAR, PETRA MARESOVA, JAMALUDDIN ABDULLAH, HAMIDREZA NAMAZI
Analysis of the brain activity in different mental tasks is an important area of research. We used complexity-based analysis to study the changes in brain activity in four mental tasks: relaxation, Stroop color-word, mirror image recognition, and arithmetic tasks. We used fractal theory, sample entropy, and approximate entropy to analyze the changes in electroencephalogram (EEG) signals between different
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CHAOS THEORY, ADVANCED METAHEURISTIC ALGORITHMS AND THEIR NEWFANGLED DEEP LEARNING ARCHITECTURE OPTIMIZATION APPLICATIONS: A REVIEW Fractals (IF 4.7) Pub Date : 2024-04-05 AKIF AKGUL, YELl̇Z KARACA, MUHAMMED ALI PALA, MURAT ERHAN ÇIMEN, ALI FUAT BOZ, MUSTAFA ZAHID YILDIZ
Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve
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EXACT SOLUTIONS AND BIFURCATION OF A MODIFIED GENERALIZED MULTIDIMENSIONAL FRACTIONAL KADOMTSEV–PETVIASHVILI EQUATION Fractals (IF 4.7) Pub Date : 2024-04-05 MINYUAN LIU, HUI XU, ZENGGUI WANG, GUIYING CHEN
In this paper, we investigate the exact solutions of a modified generalized multidimensional fractional Kadomtsev–Petviashvili (KP) equation by the bifurcation method. First, the equation is converted into a planar dynamical system through fractional complex wave transformation. The phase portraits of the equation and qualitative analysis are presented under different bifurcation conditions. Then,
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SOME ZAGREB-TYPE INDICES OF VICSEK POLYGON GRAPHS Fractals (IF 4.7) Pub Date : 2024-04-05 ZHIQIANG WU, YUMEI XUE, HUIXIA HE, CHENG ZENG, WENJIE WANG
Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability
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VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM Fractals (IF 4.7) Pub Date : 2024-04-03 YINGZI GUAN, KHALED A. GEPREEL, JI-HUAN HE
Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential
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A NEW ROUGH FRACTURE PERMEABILITY MODEL OF COAL WITH INJECTED WATER BASED ON DAMAGED TREE-LIKE BRANCHING NETWORK Fractals (IF 4.7) Pub Date : 2024-04-03 ZHEN LIU, ZHENG LI, HE YANG, JING HAN, MUYAO ZHU, SHUAI DONG, ZEHAN YU
The fracture network structure of coal is very complex, and it has always been a hot issue to characterize the fracture network structure of coal by using a tree-like branching network. In this paper, a new rough fracture permeability model of water injection coal based on a damaged tree-like branching network is proposed. In this model, fractal theory and sine wave model are used to characterize the
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DECODING OF THE EXTRAOCULAR MUSCLES ACTIVATIONS BY COMPLEXITY-BASED ANALYSIS OF ELECTROMYOGRAM (EMG) SIGNALS Fractals (IF 4.7) Pub Date : 2024-04-03 SRIDEVI SRIRAM, KARTHIKEYAN RAJAGOPAL, ONDREJ KREJCAR, HAMIDREZA NAMAZI
The analysis of extraocular muscles’ activation is crucial for understanding eye movement patterns, providing insights into oculomotor control, and contributing to advancements in fields such as vision research, neurology, and biomedical engineering. Ten subjects went through the experiments, including normal watching, blinking, upward and downward movements of eyes, and eye movements to the left and
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RESEARCH ON FRACTAL DIMENSIONS AND THE HÖLDER CONTINUITY OF FRACTAL FUNCTIONS UNDER OPERATIONS Fractals (IF 4.7) Pub Date : 2024-04-01 BINYAN YU, YONGSHUN LIANG
Based on the previous studies, we make further research on how fractal dimensions of graphs of fractal continuous functions under operations change and obtain a series of new results in this paper. Initially, it has been proven that a positive continuous function under unary operations of any nonzero real power and the logarithm taking any positive real number that is not equal to one as the base number
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INVESTIGATION ON CONCRETE MICROSTRUCTURAL EVOLUTION AND SLOPE STABILITY BASED ON COUPLED FRACTAL FLUID–STRUCTURE MODEL Fractals (IF 4.7) Pub Date : 2024-04-01 TINGTING YANG, YANG LIU, GUANNAN LIU, BOMING YU, MINGYAO WEI
Slope instability is a common type of damage in embankment dams. Analyzing its microstructural changes during water transport is beneficial to identify the critical damage point in more detail. To this end, we closely link both diffused water molecule and damaged concrete. On the basis of the original research on fractal theory, the fractal permeability model for the pore system is established. At
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FRACTAL ANALYSIS FOR PERMEABILITY OF MULTIPLE SHALE GAS TRANSPORT MECHANISMS IN ROUGHENED TREE-LIKE NETWORKS Fractals (IF 4.7) Pub Date : 2024-03-27 YIDAN ZHANG, BOQI XIAO, YANBIN WANG, GUOYING ZHANG, YI WANG, HAORAN HU, GONGBO LONG
In this work, a new gas transport model for shale reservoirs is constructed by embedding randomly distributed roughened tree-like bifurcation networks into the matrix porous medium. We constructed apparent permeability models for different shale gas flow mechanisms based on fractal theory, taking into account the effects of relative roughness and surface diffusion. The effects of bifurcation structure
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A NOVEL TRANSFORMER METHOD PRETRAINED WITH MASKED AUTOENCODERS AND FRACTAL DIMENSION FOR DIABETIC RETINOPATHY CLASSIFICATION Fractals (IF 4.7) Pub Date : 2024-03-27 YAOMING YANG, ZHAO ZHA, CHENNAN ZHOU, LIDA ZHANG, SHUXIA QIU, PENG XU
Diabetic retinopathy (DR) is one of the leading causes of blindness in a significant portion of the working population, and its damage on vision is irreversible. Therefore, rapid diagnosis on DR is crucial for saving the patient’s eyesight. Since Transformer shows superior performance in the field of computer vision compared with Convolutional Neural Networks (CNNs), it has been proposed and applied
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3D RENDERING OF THE QUATERNION MANDELBROT SET WITH MEMORY Fractals (IF 4.7) Pub Date : 2024-03-27 RICARDO FARIELLO, PAUL BOURKE, GABRIEL V. S. ABREU
In this paper, we explore the quaternion equivalent of the Mandelbrot set equipped with memory and apply various visualization techniques to the resulting 4-dimensional geometry. Three memory functions have been considered, two that apply a weighted sum to only the previous two terms and one that performs a weighted sum of all previous terms of the series. The visualization includes one or two cutting
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SOME NEW PARAMETRIZED INEQUALITIES ON FRACTAL SET Fractals (IF 4.7) Pub Date : 2024-03-27 HONGYAN XU, ABDELGHANI LAKHDARI, WEDAD SALEH, BADREDDINE MEFTAH
The aim of this study is to examine certain open three-point Newton–Cotes-type inequalities for differentiable generalized s-convex functions on a fractal set. To begin, we introduce a novel parametrized identity involving the relevant formula, which yields various new findings as well as previously established ones. Finally, an example is given to demonstrate the accuracy of the new results and their
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THE (IN)EFFICIENCY OF USA EDUCATION GROUP STOCKS: BEFORE, DURING AND AFTER COVID-19 Fractals (IF 4.7) Pub Date : 2024-03-26 LEONARDO H. S. FERNANDES, JOSÉ P. V. FERNANDES, JOSÉ W. L. SILVA, RANILSON O. A. PAIVA, IBSEN M. B. S. PINTO, FERNANDO H. A. DE ARAÚJO
This paper represents a pioneering effort to investigate multifractal dynamics that exclusively encompass the return time series of USA Education Group Stocks concerning two non-overlapping periods (before, during, and after COVID-19). Given this, we employ the Multifractal Detrended Fluctuations Analysis (MF-DFA). In this sense, we investigate the generalized Hurst exponent h(q) and the Rényi exponent
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SHORTEST PATH DISTANCE AND HAUSDORFF DIMENSION OF SIERPINSKI NETWORKS Fractals (IF 4.7) Pub Date : 2024-03-26 JIAQI FAN, JIAJUN XU, LIFENG XI
In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.
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APPLICATION OF FRACTIONAL-ORDER INTEGRAL TRANSFORMS IN THE DIAGNOSIS OF ELECTRICAL SYSTEM CONDITIONS Fractals (IF 4.7) Pub Date : 2024-03-26 H. M. CORTÉS CAMPOS, J. F. GÓMEZ-AGUILAR, C. J. ZÚÑIGA-AGUILAR, L. F. AVALOS-RUIZ, J. E. LAVÍN-DELGADO
This paper proposes a methodology for the diagnosis of electrical system conditions using fractional-order integral transforms for feature extraction. This work proposes three feature extraction algorithms using the Fractional Fourier Transform (FRFT), the Fourier Transform combined with the Mittag-Leffler function, and the Wavelet Transform (WT). Each algorithm extracts data from an electrical system
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COMPLEX NETWORKS GENERATED BY A SELF-SIMILAR PLANAR FRACTAL Fractals (IF 4.7) Pub Date : 2024-03-26 QIN WANG, WENJIA MA, KEQIN CUI, QINGCHENG ZENG, LIFENG XI
Many complex networks have scale-free and small-world effects. In this paper, a family of evolving networks is constructed modeled by a non-symmetric self-similar planar fractal, using the encoding method in fractal geometry. Based on the self-similar structure, we study the degree distribution, clustering coefficient and average path length of our evolving network to verify their scale-free and small-world
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ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS Fractals (IF 4.7) Pub Date : 2024-03-22 YU PENG, TINGSONG DU
In this paper, we propose a fresh conception about convexity, known as the multiplicative (s,P)-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the ∗differentiable (s,P)-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and
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HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL Fractals (IF 4.7) Pub Date : 2024-03-05 HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA
Fractional q-calculus is considered to be the fractional analogs of q-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) q-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving ℏ-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF q-integral. The results not only
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RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES Fractals (IF 4.7) Pub Date : 2024-02-28 JUNJIE LEI, MEIHONG LIU
Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective
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A FRACTAL-FRACTIONAL TSUNAMI MODEL CONSIDERING NEAR-SHORE FRACTAL BOUNDARY Fractals (IF 4.7) Pub Date : 2024-02-28 YAN WANG, WEIFAN HOU, KHALED GEPREEL, HONGJU LI
Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal
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THREE PROPERTIES OF FRACTAL NETWORKS BASED ON BEDFORD–MCMULLEN CARPET Fractals (IF 4.7) Pub Date : 2024-02-27 JIAN ZHENG, CHENG ZENG, YUMEI XUE, XIAOHAN LI
In this paper, we consider the networks modeled by several self-affine sets based on the Bedford–Mcmullen carpet. We calculate three properties of the networks, including the cumulative degree distribution, the average clustering coefficient and the average path length. We show that such networks have scale-free and small-world effects.
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THE IMPACT OF GLOBAL DYNAMICS ON THE FRACTALS OF A QUADROTOR UNMANNED AERIAL VEHICLE (QUAV) CHAOTIC SYSTEM Fractals (IF 4.7) Pub Date : 2024-02-27 MUHAMMAD MARWAN, MAOAN HAN, YANFEI DAI, MEILAN CAI
In this paper, we have extended the concept of advanced Julia function for the discovery of new type of trajectories existing inside outer and inner wings. A dynamical system based on four rotors, referred to as quadrotor unmanned aerial vehicle (QUAV), is considered for the first time to seek the generation of extra wings using fractal theory. Moreover, we have used Julia and advanced Julia function
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DENG ENTROPY AND INFORMATION DIMENSION FOR COVID-19 AND COMMON PNEUMONIA CLASSIFICATION Fractals (IF 4.7) Pub Date : 2024-02-24 PILAR ORTIZ-VILCHIS, MAYRA ANTONIO-CRUZ, MINGLI LEI, ALDO RAMIREZ-ARELLANO
Motivated by previous authors’ work, where Shannon entropy, box covering and information dimension were applied to quantify pulmonary lesions, this paper extends such a contribution in two fashions: (i) Following the approach to quantify pulmonary lesions with Deng entropy and Deng information dimension obtained through box covering method; (ii) exploiting the Shannon and Deng lesion quantification
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A 3D FRACTAL MODEL COUPLED WITH TRANSPORT AND ACTION MECHANISMS TO PREDICT THE APPARENT PERMEABILITY OF SHALE MATRIX Fractals (IF 4.7) Pub Date : 2024-02-23 SIYUAN WANG, PENG HOU, XIN LIANG, SHANJIE SU, QUANSHENG LIU
The permeability of shale controls gas transport in shale gas reservoirs. The shale has a complex pore structure at the nanoscale and its permeability is affected by multiple transport and action mechanisms. In this study, a 3D fractal model for predicting the apparent gas permeability of shale matrix is presented, accounting for the effects of the transport mechanisms (bulk gas transport and adsorption
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A STUDY OF FRACTAL DUAL MOMENTUM INVESTMENT STRATEGY UNDER THE CONSTRAINT OF MULTI-FRACTAL CHARACTERISTICS OF STOCK MARKET Fractals (IF 4.7) Pub Date : 2024-02-23 XU WU, PEIYU WANG, CHI YANG, YAN XIAO
Since the discovery of momentum effect, people have started the journey of using the momentum effect to construct momentum strategies. As a result of coupling cross-sectional and time-series momentum strategy, dual momentum strategy (DM strategy) has been widely used in practice and closely followed by academics. To address the shortcoming of the classical DM strategy that has not considered the multi-fractal
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MULTIFRACTAL CHARACTERIZATION OF THE INHOMOGENEOUS STRAIN EVOLUTION OF THE DEHYDRATED COAL: INSIGHT FROM COAL MICROSTRUCTURE Fractals (IF 4.7) Pub Date : 2024-02-22 JUNJUN FENG, CHUANHUA XU, FENG YU, JUN PENG, QISONG HUANG, PENG JIN
Underground coal mining in China has gradually moved into deeper seams in recent years, which results in a higher ambient temperature in the mining space and significantly affects the mechanical behavior of coal. In this study, dehydrated coal samples were obtained at different temperatures ranging from 30∘ to 70∘, and the mechanical behavior of the dehydrated coal was investigated through compressive
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NOVEL PERSPECTIVE TO THE FRACTIONAL SCHRÖDINGER EQUATION ARISING IN OPTICAL FIBERS Fractals (IF 4.7) Pub Date : 2024-02-20 KANG-LE WANG
In this paper, the fractional Schrödinger equation is described with beta derivative, which is used to elucidate the dynamic interaction of ultra-short pulses with quantum properties in optical fibers. This work is to study the solitary wave and periodic solutions of the fractional Schrödinger equation by employing three powerful and simple mathematical approaches like fractional Kudryashov method
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A d-SUMMABLE APPROACH TO DENG INFORMATION DIMENSION OF COMPLEX NETWORKS Fractals (IF 4.7) Pub Date : 2024-02-19 ALDO RAMIREZ-ARELLANO, JUAN BORY-REYES
Several new network information dimension definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. This paper proposes a new definition based on Deng entropy and d-summability (a concept from geometric measure theory). We will prove to what extent the new formulation will be useful in the theoretical and applied points of view.
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A CLUSTERED FRACTAL DISCRETE FRACTURE NETWORK MODEL FOR FRACTURED COAL Fractals (IF 4.7) Pub Date : 2024-02-16 XIN LIANG, PENG HOU, GUANNAN LIU, YI XUE, JIA LIU, FENG GAO, ZHIZHEN ZHANG
The fracture network in fractured coal is the main channel of coal seam gas flow. Not only the geometric topology properties (such as fractal characteristics) of a single fracture but also the connection topology properties (interconnection characteristics between fractures) of the fracture network have an important impact on the fluid flow in fracture networks. In this study, the connection topology
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A FRACTAL MODIFICATION OF THE PSEUDO-PARABOLIC EQUATION AND ITS GENERALIZED FRACTAL VARIATIONAL PRINCIPLE Fractals (IF 4.7) Pub Date : 2024-02-14 KANG-JIA WANG, SHUAI LI, PENG XU, FENG SHI
In this work, a new fractal pseudo-parabolic equation is derived by means of He’s fractal derivative. The semi-inverse method (SIM) is employed to develop the generalized fractal variational principle (GFVP), which can reveal the energy conservation law in the fractal space and provide some new insights on the study of the variational method.
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PHYSICS-INFORMED DEEP AI SIMULATION FOR FRACTAL INTEGRO-DIFFERENTIAL EQUATION Fractals (IF 4.7) Pub Date : 2024-01-31 XUEJUAN LI, RUI ZHAO
Fractal integro-differential equations (IDEs) can describe the effect of local microstructure on a complex physical problem, however, the traditional numerical methods are not suitable for solving the new-born models with the fractal integral and fractal derivative. Here we show that deep learning can be used to solve the bottleneck. By the two-scale transformation, the fractal IDE is first approximately
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MULTIPARENT FRACTAL IMAGE CODING-BASED METHODS FOR SALT-AND-PEPPER NOISE REMOVAL Fractals (IF 4.7) Pub Date : 2024-01-27 WEIJIE LIANG, XIAOYI LI, ZHIHUI TU, JIAN LU
Salt-and-pepper noise consists of outlier pixel values which significantly impair image structure and quality. Multiparent fractal image coding (MFIC) methods substantially exploit image redundancy by utilizing multiple domain blocks to approximate the range block, partially compensating for the information loss caused by noise. Motivated by this, we propose two novel image restoration methods based
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EXPLORING INSECTS FREE FLIGHT: ENHANCING THE DIPTERAN FLIGHT MODEL TO INCLUDE FRACTAL EFFECTS Fractals (IF 4.7) Pub Date : 2024-01-27 ALEX ELÍAS-ZÚÑIGA, OSCAR MARTÍNEZ-ROMERO, DANIEL OLVERA-TREJO, IMPERIO ANEL PERALES-MARTÍNEZ, LUIS MANUEL PALACIOS-PINEDA
This paper advances fundamental knowledge of how environmental conditions and physical phenomena at different scales can be included in the differential equation that models the flight dynamics of dipteran insects. The insect’s anatomical capability of modifying their mass inertia and flapping-wing damping properties during flight are included by modeling inertia and damping forces with fractal derivatives
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MEASURING STRUCTURAL CHANGES OF RECURRENCE PATTERNS IN MULTIFRACTAL AND MULTISCALE ASPECTS BY GENERALIZED RECURRENCE LACUNARITY Fractals (IF 4.7) Pub Date : 2024-01-27 XUEGENG MAO, ZEZHOU LIU, JINZHAO LIU, WANRU XIE, PENGJIAN SHANG, ZHIWEI SHAO
Recurrence lacunarity has been recently proposed to detect dynamical state transitions over various temporal scales. In this paper, we combine suggested distribution moments and introduce multifractal recurrence lacunarity to unearth rich information of trajectories in phase space. By considering generalized moments, it provides an enhanced measurement to account for differences of black pixels in
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FRACTAL STUDY ON THE PERMEABILITY IN CHARGED MICRO-FRACTURED POROUS MEDIA Fractals (IF 4.7) Pub Date : 2024-01-27 WENYAN LIU, YUZENG DUAN, BOQI XIAO, LIANG LUO, MINGQING ZOU, MINGCHAO LIANG
Fractured porous media is of great significance to the exploration and development of unconventional reservoirs. In this paper, a fractal model for permeability through micro-fractured porous media with consideration of the electric double layer (EDL) effect is proposed based on the fractal theory. The present model indicates that the permeability is a function of the electrokinetic parameters and
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THE MULTI-PARAMETER FRACTAL–FRACTIONAL INEQUALITIES FOR FRACTAL (P,m)-CONVEX FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-01-27 XIAOMAN YUAN, HÜSEYIN BUDAK, TINGSONG DU
Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal–fractional integral inequalities containing the fractal (P,m)-convex functions. Initially, we formulate the new conception of the fractal (P,m)-convex functions and work on a variety of properties
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RESEARCH ON THE K-DIMENSION OF THE SUM OF TWO CONTINUOUS FUNCTIONS AND ITS APPLICATION Fractals (IF 4.7) Pub Date : 2024-01-27 Y. X. CAO, N. LIU, Y. S. LIANG
In this paper, we have done some research studies on the fractal dimension of the sum of two continuous functions with different K-dimensions and approximation of s-dimensional fractal functions. We first investigate the K-dimension of the linear combination of fractal function whose K-dimension is s and the function satisfying Lipschitz condition is still s-dimensional. Then, based on the research
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ON THE ASYMPTOTIC STABILITY OF A NEW FRACTIONAL-ORDER SLIDING MODE CONTROL WITH APPLICATION TO ROBOTIC SYSTEMS Fractals (IF 4.7) Pub Date : 2024-01-27 FATMA ABDELHEDI, RIM JALLOULI KHLIF, AHMED SAID NOURI, NABIL DERBEL
This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally
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SOLVABILITY AND OPTIMAL CONTROL OF A SYSTEM OF SEMILINEAR NONLOCAL FRACTIONAL EVOLUTION INCLUSIONS WITH PARTIAL CLARKE SUBDIFFERENTIAL Fractals (IF 4.7) Pub Date : 2024-01-24 LU-CHUAN CENG, BOLING CHEN, SHANLI LIAO, VAN THIEN NGUYEN, JEN-CHIH YAO
The purpose of this paper is to deal with a system governed by a system of semilinear nonlocal fractional evolution inclusions with partial Clarke subdifferential and its optimal control. First, we establish an existence theorem of the mild solution for the presented control system by applying the measure of noncompactness, a fixed point theorem of a condensing multivalued map and some properties of
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ON THE SEMI-DOMAIN SOLITON SOLUTIONS FOR THE FRACTAL (3+1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI– BOUSSINESQ EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 KANG-JIA WANG, JING-HUA LIU, FENG SHI
The aim of this study is to explore some semi-domain soliton solutions for the fractal (3+1)-dimensional generalized Kadomtsev–Petviashvili–Boussinesq equation (GKPBe) within He’s fractal derivative. First, the fractal soliton molecules are plumbed by combining the Hirota equation and fractal two-scale transform. Second, the Bernoulli sub-equation function approach together with the fractal two-scale
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A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 KANG-JIA WANG, FENG SHI
The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the LTδ(Ξδ) and LCδ(Ξδ) functions that are derived on the basis of the Mittag-Leffler function (MLF)
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APPLICATION OF VARIATIONAL PRINCIPLE AND FRACTAL COMPLEX TRANSFORMATION TO (3+1)-DIMENSIONAL FRACTAL POTENTIAL-YTSF EQUATION Fractals (IF 4.7) Pub Date : 2024-01-23 JUNFENG LU
This paper focuses on the numerical investigation of the fractal modification of the (3+1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation. A variational approach based on the two-scale fractal complex transformation and the variational principle is presented for solving this fractal equation. The fractal potential-YTSF equation can be transformed as the original potential-YTSF equation
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EDGE-WIENER INDEX OF SIERPINSKI FRACTAL NETWORKS Fractals (IF 4.7) Pub Date : 2024-01-23 YIQI YAO, CAIMIN DU, LIFENG XI
The edge-Wiener index, an invariant index representing the summation of the distances between every pair of edges in the graph, has monumental influence on the study of chemistry and materials science. In this paper, drawing inspiration from Gromov’s idea, we use the finite pattern method proposed by Wang et al. [Average geodesic distance of Sierpinski gasket and Sierpinski networks, Fractals 25(5)
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FRACTAL ORACLE NUMBERS Fractals (IF 4.7) Pub Date : 2024-01-23 JOEL RATSABY
Consider orbits 𝒪(z,κ) of the fractal iterator fκ(z):=z2+κ, κ∈ℂ, that start at initial points z∈K̂κ(m)⊂ℂ̂, where ℂ̂ is the set of all rational complex numbers (their real and imaginary parts are rational) and K̂κ(m) consists of all such z whose complexity does not exceed some complexity parameter value m (the complexity of z is defined as the number of bits that suffice to describe the real and imaginary
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QUALITATIVE AND STABILITY ANALYSIS WITH LYAPUNOV FUNCTION OF EMOTION PANIC SPREADING MODEL INSIGHT OF FRACTIONAL OPERATOR Fractals (IF 4.7) Pub Date : 2024-01-19 PEILUAN LI, CHANGJIN XU, MUHAMMAD FARMAN, ALI AKGUL, YICHENG PANG
In an emergency, fear can spread among crowds through one-on-one encounters, with negative societal consequences. The purpose of this research is to create a novel theoretical model of fear (panic) spread in the context of epidemiology during an emergency using the fractal fractional operator. For quantitative analysis, the system’s boundedness and positivity are checked. According to the Arzela Ascoli
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CONSTRUCTION OF A WEIGHTED FRACTAL INTERPOLATION SURFACE BASED ON MATKOWSKI CONTRACTIONS Fractals (IF 4.7) Pub Date : 2024-01-18 QIAN-RUI ZHONG, HONG-YONG WANG
In this paper, we construct a new kind of weighted recursive iteration function system (IFS) and prove the existence of the unique attractor for the kind of IFS based on the Matkowski fixed point theorem. We confirm that the attractor is a bivariate fractal interpolation surface (FIS), which interpolates a given set of data. In addition, we also provide an upper error estimate of such FISs caused by