Fractal and Fractional最新文献_第4页

Complex-Valued Suprametric Spaces, Related Fixed Point Results, and Their Applications to Barnsley Fern Fractal Generation and Mixed Volterra–Fredholm Integral Equations 复值超对称空间、相关定点结果及其在巴恩斯利蕨分形生成和混合 Volterra-Fredholm 积分方程中的应用

Fractal and Fractional Pub Date : 2024-07-12 DOI: 10.3390/fractalfract8070410

S. K. Panda, V. Vijayakumar, Ravi P. Agarwal

{"title":"Complex-Valued Suprametric Spaces, Related Fixed Point Results, and Their Applications to Barnsley Fern Fractal Generation and Mixed Volterra–Fredholm Integral Equations","authors":"S. K. Panda, V. Vijayakumar, Ravi P. Agarwal","doi":"10.3390/fractalfract8070410","DOIUrl":"https://doi.org/10.3390/fractalfract8070410","url":null,"abstract":"The novelty of this work is that it is the first to introduce complex-valued suprametric spaces and apply it to Fractal Generation and mixed Volterra–Fredholm Integral Equations. In the realm of fuzzy logic, complex-valued suprametric spaces provide a robust framework for quantifying the similarity between fuzzy sets; for instance, utilizing a complex-valued suprametric approach, we compared the similarity between fuzzy sets represented by complex-valued feature vectors, yielding quantitative measures of their relationships. Thereafter, we establish related fixed point results and their applications in algorithmic and numerical contexts. The study then delves into the generation of fractals, exemplified by the Barnsley Fern fractal, utilizing sequences of affine transformations within complex-valued suprametric spaces. Moreover, this article presents two algorithms for soft computing and fractal generation. The first algorithm uses complex-valued suprametric similarity for fuzzy clustering, iteratively assigning fuzzy sets to clusters based on similarity and updating cluster centers until convergence. The distinctive pattern of the Barnsley Fern fractal is produced by the second algorithm’s repetitive affine transformations, which are chosen at random. These techniques demonstrate how well complex numbers cluster and how simple procedures can create complicated fractals. Moving beyond fractal generation, the paper addresses the solution of mixed Volterra–Fredholm integral equations in the complex plane using our results, demonstrating numerical illustrations of complex-valued integral equations.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"58 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141652676","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 Non-Local Integro-Differential Equations with Hadamard Fractional Derivatives: Existence, Uniqueness, and Stability in the Context of RLC Models 哈达玛分式微分方程的非局部积分微分方程分析：RLC 模型背景下的存在性、唯一性和稳定性

Fractal and Fractional Pub Date : 2024-07-12 DOI: 10.3390/fractalfract8070409

Manigandan Murugesan, Saravanan Shanmugam, Mohamed Rhaima, Ragul Ravi

引用次数: 0

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators 由一类运算符定义的可接受函数类的模糊微分从属关系

Fractal and Fractional Pub Date : 2024-07-11 DOI: 10.3390/fractalfract8070405

Ekram E. Ali, Miguel Vivas-Cortez, R. El-Ashwah

引用次数: 0

Damage Law and Reasonable Width of Coal Pillar under Gully Area: Linking Fractal Characteristics of Coal Pillar Fractures to Their Stability 沟域下煤柱破坏规律及合理宽度煤柱断裂的分形特征与其稳定性的联系

Fractal and Fractional Pub Date : 2024-07-11 DOI: 10.3390/fractalfract8070407

Zhaopeng Wu, Yunpei Liang, Kaijun Miao, Qigang Li, Sichen Liu, Qican Ran, Wanjie Sun, Hualong Yin, Yun Ma

{"title":"Damage Law and Reasonable Width of Coal Pillar under Gully Area: Linking Fractal Characteristics of Coal Pillar Fractures to Their Stability","authors":"Zhaopeng Wu, Yunpei Liang, Kaijun Miao, Qigang Li, Sichen Liu, Qican Ran, Wanjie Sun, Hualong Yin, Yun Ma","doi":"10.3390/fractalfract8070407","DOIUrl":"https://doi.org/10.3390/fractalfract8070407","url":null,"abstract":"The coal pillar is an important structure to control the stability of the roadway surrounding rock and maintain the safety of underground mining activities. An unreasonable design of the coal pillar size can result in the failure of the surrounding rock structure or waste of coal resources. The northern Shaanxi mining area of China belongs to the shallow buried coal seam mining in the gully area, and the gully topography makes the bearing law of the coal pillar and the development law of the internal fracture more complicated. In this study, based on the geological conditions of the Longhua Mine 20202 working face, a PFC2D numerical model was established to study the damage characteristics of coal pillars under the different overlying strata base load ratios in the gentle terrain area and the different gully slope sections in the gully terrain area, and the coal pillar design strategy based on the fractal characteristics of the fractures was proposed to provide a reference for determining the width of the coal pillars in mines under similar geological conditions. The results show that the reliability of the mathematical equation between the overlying strata base load ratio and the fractal dimension of the fractures in the coal pillar is high, the smaller the overlying strata base load ratio is, the greater the damage degree of the coal pillar is, and the width of the coal pillar of 15 m under the condition of the actual overlying strata base load ratio (1.19) is more reasonable. Compared with the gentle terrain area, the damage degree of the coal pillar in the gully terrain area is larger, in which the fractal dimension of the fracture in the coal pillar located below the gully bottom is the smallest, and the coal pillar in the gully terrain should be set as far as possible to make the coal pillar located below the gully bottom, so as to ensure the stability of the coal pillar.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"124 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141656964","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

Fractional Hermite–Hadamard–Mercer-Type Inequalities for Interval-Valued Convex Stochastic Processes with Center-Radius Order and Their Related Applications in Entropy and Information Theory 具有中心-半径阶的区间值凸随机过程的分数赫米特-哈达玛-默塞尔式不等式及其在熵和信息论中的相关应用

Fractal and Fractional Pub Date : 2024-07-11 DOI: 10.3390/fractalfract8070408

Ahsan Fareed Shah, Serap Özcan, Miguel Vivas-Cortez, Muhammad Shoaib Saleem, A. Kashuri

引用次数: 0

Derivation of Closed-Form Expressions in Apéry-like Series Using Fractional Calculus and Applications 使用分式微积分推导阿佩里样数列中的闭式表达式及其应用

Fractal and Fractional Pub Date : 2024-07-11 DOI: 10.3390/fractalfract8070406

Ampol Duangpan, Ratinan Boonklurb, Udomsak Rakwongwan, Phiraphat Sutthimat

引用次数: 0

Performance Analysis of Fully Intuitionistic Fuzzy Multi-Objective Multi-Item Solid Fractional Transportation Model 全直觉模糊多目标多项目固体分数运输模型的性能分析

Fractal and Fractional Pub Date : 2024-07-09 DOI: 10.3390/fractalfract8070404

Sultan Almotairi, E. Badr, M. Elsisy, F. Farahat, M. El Sayed

{"title":"Performance Analysis of Fully Intuitionistic Fuzzy Multi-Objective Multi-Item Solid Fractional Transportation Model","authors":"Sultan Almotairi, E. Badr, M. Elsisy, F. Farahat, M. El Sayed","doi":"10.3390/fractalfract8070404","DOIUrl":"https://doi.org/10.3390/fractalfract8070404","url":null,"abstract":"An investigation is conducted in this paper into a performance analysis of fully intuitionistic fuzzy multi-objective multi-item solid fractional transport model (FIF-MMSFTM). It is to be anticipated that the parameters of the conveyance model will be imprecise by virtue of numerous uncontrollable factors. The model under consideration incorporates intuitionistic fuzzy (IF) quantities of shipments, costs and profit coefficients, supplies, demands, and transport. The FIF-MMSFTM that has been devised is transformed into a linear form through a series of operations. The accuracy function and ordering relations of IF sets are then used to reduce the linearized model to a concise multi-objective multi-item solid transportation model (MMSTM). Furthermore, an examination is conducted on several theorems that illustrate the correlation between the FIF-MMSFTM and its corresponding crisp model, which is founded upon linear, hyperbolic, and parabolic membership functions. A numerical example was furnished to showcase the efficacy and feasibility of the suggested methodology. The numerical data acquired indicates that the linear, hyperbolic, and parabolic models require fewer computational resources to achieve the optimal solution. The parabolic model has the greatest number of iterations, in contrast to the hyperbolic model which has the fewest. Additionally, the elapsed run time for the three models is a negligible amount of time: 0.2, 0.15, and 1.37 s, respectively. In conclusion, suggestions for future research are provided.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"98 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664307","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

Applications of Fractional-Order Calculus in Robotics 分阶微积分在机器人学中的应用

Fractal and Fractional Pub Date : 2024-07-06 DOI: 10.3390/fractalfract8070403

A. Singh, Kishore Bingi

引用次数: 0

Split-Step Galerkin FE Method for Two-Dimensional Space-Fractional CNLS 二维空间-分数 CNLS 的分步 Galerkin FE 方法

Fractal and Fractional Pub Date : 2024-07-05 DOI: 10.3390/fractalfract8070402

Xiaogang Zhu, Yaping Zhang, Yufeng Nie

引用次数: 0

Employing the Laplace Residual Power Series Method to Solve (11)- and (21)-Dimensional Time-Fractional Nonlinear Differential Equations++ 用拉普拉斯残差幂级数法求解(11)和(21)维时间分数非线性微分方程++

Fractal and Fractional Pub Date : 2024-07-04 DOI: 10.3390/fractalfract8070401

Adel R. Hadhoud, Abdulqawi A. M. Rageh, T. Radwan

引用次数: 0