Fractal and Fractional最新文献_第8页

Contributions to the Numerical Solutions of a Caputo Fractional Differential and Integro-Differential System 对卡普托分微分和积分微分系统数值解法的贡献

Fractal and Fractional Pub Date : 2024-03-29 DOI: 10.3390/fractalfract8040201

Abdelkader Moumen, A. Mennouni, Mohamed Bouye

引用次数: 0

Fractal Operators and Convergence Analysis in Fractional Viscoelastic Theory 分数粘弹性理论中的分形算子和收敛分析

Fractal and Fractional Pub Date : 2024-03-29 DOI: 10.3390/fractalfract8040200

X. Yu, Yajun Yin

引用次数: 0

Fractal Analysis of Polarizability in Graphite Deposits: Methodological Integration for Geological Prediction and Exploration Efficiency 石墨矿床极化性的分形分析：地质预测与勘探效率的方法整合

Fractal and Fractional Pub Date : 2024-03-29 DOI: 10.3390/fractalfract8040198

Yuqi Liang, Qinglin Xia, Kenan Jiang, Ercheng Pang

{"title":"Fractal Analysis of Polarizability in Graphite Deposits: Methodological Integration for Geological Prediction and Exploration Efficiency","authors":"Yuqi Liang, Qinglin Xia, Kenan Jiang, Ercheng Pang","doi":"10.3390/fractalfract8040198","DOIUrl":"https://doi.org/10.3390/fractalfract8040198","url":null,"abstract":"Most geophysical and geochemical data are commonly acknowledged to exhibit fractal and multifractal properties, but the fractal characteristics of polarizability have received limited attention from the literature. The present study demonstrates that the polarizability data of the graphite deposits have fractal characteristics and introduces the fractal method for its quantitative analysis to indicate and predict the properties of graphite deposits. The results show that the concentration-area (C-A) method is superior to classical interpolation in anomaly extraction but inferior to the spectrum-area (S-A) method in the coverage region. Because the type of graphite ore is sedimentary-metamorphic in this area, the graphite ore-bodies can be regarded as a special stratum, which is different from most metal deposits, and the anomaly of graphite ore are shown in the background mode of the S-A method. The high values of the background mode effectively indicate the potential areas where the graphite-bearing strata occur, while observing a decrease in the power-law exponent (β) of the background mode as the width of ore-bodies increases. The validity of this conclusion was confirmed based on the vertical profiles of the predicted area, and the uncharted ore vein was thereby identified. Furthermore, it was found that the anomaly mode can serve as a grade indicator of graphite ore rather than delineating the fault. By integrating the background and anomaly modes of the S-A method, we can quantitatively predict and effectively identify high-grade targets from sedimentary deposits containing minerals in future exploration.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"47 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367989","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

New Generalized Jacobi Polynomial Galerkin Operational Matrices of Derivatives: An Algorithm for Solving Boundary Value Problems 新的广义雅可比多项式 Galerkin 衍生运算矩阵：解决边界值问题的算法

Fractal and Fractional Pub Date : 2024-03-29 DOI: 10.3390/fractalfract8040199

H. M. Ahmed

引用次数: 0

Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations 单孔、双孔和四孔几何非线性振荡器全局动力学比较

Fractal and Fractional Pub Date : 2024-03-29 DOI: 10.3390/fractalfract8040202

Huihang Sun, H. Shang

引用次数: 0

A Quasilinearization Approach for Identification Control Vectors in Fractional-Order Nonlinear Systems 分数阶非线性系统中识别控制向量的准线性化方法

Fractal and Fractional Pub Date : 2024-03-28 DOI: 10.3390/fractalfract8040196

M. Koleva, L. Vulkov

引用次数: 0

Fundamental Matrix, Integral Representation and Stability Analysis of the Solutions of Neutral Fractional Systems with Derivatives in the Riemann—Liouville Sense 黎曼-刘维尔意义上带衍生的中性分数系统解的基本矩阵、积分表示和稳定性分析

Fractal and Fractional Pub Date : 2024-03-28 DOI: 10.3390/fractalfract8040195

H. Kiskinov, Mariyan Milev, Slav I. Cholakov, A. Zahariev

{"title":"Fundamental Matrix, Integral Representation and Stability Analysis of the Solutions of Neutral Fractional Systems with Derivatives in the Riemann—Liouville Sense","authors":"H. Kiskinov, Mariyan Milev, Slav I. Cholakov, A. Zahariev","doi":"10.3390/fractalfract8040195","DOIUrl":"https://doi.org/10.3390/fractalfract8040195","url":null,"abstract":"The paper studies a class of nonlinear disturbed neutral linear fractional systems with derivatives in the the Riemann–Liouville sense and distributed delays. First, it is proved that the initial problem for these systems with discontinuous initial functions under some natural assumptions possesses a unique solution. The assumptions used for the proof are similar to those used in the case of systems with first-order derivatives. Then, with the obtained result, we derive the existence and uniqueness of a fundamental matrix and a generalized fundamental matrix for the homogeneous system. In the linear case, via these fundamental matrices we obtain integral representations of the solutions of the homogeneous system and the corresponding inhomogeneous system. Furthermore, for the fractional systems with Riemann–Liouville derivatives we introduce a new concept for weighted stabilities in the Lyapunov, Ulam–Hyers, and Ulam–Hyers–Rassias senses, which coincides with the classical stability concepts for the cases of integer-order or Caputo-type derivatives. It is proved that the zero solution of the homogeneous system is weighted stable if and only if all its solutions are weighted bounded. In addition, for the homogeneous system it is established that the weighted stability in the Lyapunov and Ulam–Hyers senses are equivalent if and only if the inequality appearing in the Ulam–Hyers definition possess only bounded solutions. Finally, we derive natural sufficient conditions under which the property of weighted global asymptotic stability of the zero solution of the homogeneous system is preserved under nonlinear disturbances.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"129 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369618","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

Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus 通过传统三轴仪器实现真正三轴应力路径的玻璃珠测试

Fractal and Fractional Pub Date : 2024-03-28 DOI: 10.3390/fractalfract8040193

Xuefeng Li, Jiahui Ma, Longlong Lv

{"title":"Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus","authors":"Xuefeng Li, Jiahui Ma, Longlong Lv","doi":"10.3390/fractalfract8040193","DOIUrl":"https://doi.org/10.3390/fractalfract8040193","url":null,"abstract":"The impact of fabric anisotropy, fractal dimension, and breakage on the strength and deformation of granular materials were diminished by uniform-size spherical glass beads. Triaxial drained and undrained tests were performed on glass beads based on a novel method to substitute true triaxial stress paths with conventional triaxial apparatus equivalents with varying intermediate principal stress coefficients (b-values). The result indicates that all specimens manifested a noticeable strain-softening phenomenon. The peak strength decreased with increasing b-value, and the specimens showed more pronounced dilatancy. This pattern is similar to the results of the true triaxial test in current research. Compared to the undrained test, the peak friction angle in the drained test displayed a greater variation with varying b-values, which indicated that the mechanical response of glass beads is sensitive to water. This difference provides experimental evidence for comprehending effective stress in granular materials with constant friction coefficients. The experiments reflect the effect of b-value changes on the p-q stress path, as well as on the peak stress ratio, the state transition stress ratio, and the critical state stress ratio. The specimens exhibited a distinct shear band at different b-values ranging from 0.2 to 0.6, which is different from observations in conventional triaxial tests for granular materials.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"51 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140373551","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

Evolving Patterns in Irrational Numbers Using Waiting Times between Digits 利用数位间的等待时间演化无理数的模式

Fractal and Fractional Pub Date : 2024-03-28 DOI: 10.3390/fractalfract8040197

Samuel Toluwalope Ogunjo, Holger Kantz

引用次数: 0

Existence of Solutions for the Initial Value Problem with Hadamard Fractional Derivatives in Locally Convex Spaces 局部凸空间中带有哈达玛分式衍生物的初值问题解的存在性

Fractal and Fractional Pub Date : 2024-03-27 DOI: 10.3390/fractalfract8040191

Weiwei Liu, Lishan Liu

引用次数: 0