Fractal and Fractional最新文献_第7页

Qualitative Analysis of RLC Circuit Described by Hilfer Derivative with Numerical Treatment Using the Lagrange Polynomial Method 用拉格朗日多项式方法对Hilfer导数描述的RLC电路进行定性分析和数值处理

2区数学

Fractal and Fractional Pub Date : 2023-11-04 DOI: 10.3390/fractalfract7110804

Naveen S., Parthiban V., Mohamed I. Abbas

引用次数: 0

An Investigation on Fractal Characteristics of the Superposition of Fractal Surfaces 分形曲面叠加的分形特性研究

2区数学

Fractal and Fractional Pub Date : 2023-11-04 DOI: 10.3390/fractalfract7110802

Xuefei Wang

引用次数: 0

Pore-Type-Dependent Fractal Features of Shales and Implications on Permeability 页岩孔隙分形特征及其对渗透率的影响

2区数学

Fractal and Fractional Pub Date : 2023-11-04 DOI: 10.3390/fractalfract7110803

Qian Zhang, Yanhui Dong, Shaoqing Tong

{"title":"Pore-Type-Dependent Fractal Features of Shales and Implications on Permeability","authors":"Qian Zhang, Yanhui Dong, Shaoqing Tong","doi":"10.3390/fractalfract7110803","DOIUrl":"https://doi.org/10.3390/fractalfract7110803","url":null,"abstract":"Pore structure features govern the capacity of gas storage and migration in shales and are highly dependent on the types of pores, i.e., interparticle (InterP) pores, intraparticle (IntraP) pores and organic matter (OM)-hosted pores. However, fractal features in terms of pore types and their respective contributions to permeability have been rarely addressed. On the basis of high-resolution imaging, fractal dimensions (Ds) have been determined from both pore size distributions and digital rock to quantify the heterogeneity in pore morphology and spatial textures. Overall, OM-hosted pores are smaller in size and more abundant in quantity, corresponding to a relatively high D, while IntraP pores are mainly isolated and scarce, translating into lower D values. Additionally, crack-like InterP pores with a moderate level of porosity and the D can play a pivotal role in shale seepage potential. A comparison of the estimated permeability among different pore types highlights that the contribution of interconnected OM pores to the overall permeability remains constrained unless they can link neighboring pore clusters, as commonly observed in organo-clay composites. Furthermore, the pore morphology and fractal features of shale rocks can exhibit noteworthy variations subjected to sedimentology, mineralogy, diagenesis and OM maturation.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"39 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135773647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional Complex Euler–Lagrange Equation: Nonconservative Systems 分数复欧拉-拉格朗日方程:非保守系统

2区数学

Fractal and Fractional Pub Date : 2023-11-02 DOI: 10.3390/fractalfract7110799

Antonela Toma, Octavian Postavaru

引用次数: 0

Existence of Solutions for Coupled System of Sequential Liouville–Caputo-Type Fractional Integrodifferential Equations 序列liouville - caputo型分数阶积分微分方程耦合系统解的存在性

2区数学

Fractal and Fractional Pub Date : 2023-11-02 DOI: 10.3390/fractalfract7110800

Manigandan Murugesan, Subramanian Muthaiah, Rajarathinam Vadivel, Bundit Unyong

引用次数: 0

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term 求解源项识别二维分数扩散逆问题的并行算法

2区数学

Fractal and Fractional Pub Date : 2023-11-02 DOI: 10.3390/fractalfract7110801

Elena N. Akimova, Murat A. Sultanov, Vladimir E. Misilov, Yerkebulan Nurlanuly

引用次数: 0

Maximum Principle for Variable-Order Fractional Conformable Differential Equation with a Generalized Tempered Fractional Laplace Operator 具有广义调质分数阶拉普拉斯算子的变阶分数阶可合微分方程的极大值原理

2区数学

Fractal and Fractional Pub Date : 2023-11-01 DOI: 10.3390/fractalfract7110798

Tingting Guan, Lihong Zhang

引用次数: 0

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space 复空间中求解分数阶非线性积分-微分方程的新方法

2区数学

Fractal and Fractional Pub Date : 2023-10-31 DOI: 10.3390/fractalfract7110796

Amnah E. Shammaky, Eslam M. Youssef, Mohamed A. Abdou, Mahmoud M. ElBorai, Wagdy G. ElSayed, Mai Taha

{"title":"A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space","authors":"Amnah E. Shammaky, Eslam M. Youssef, Mohamed A. Abdou, Mahmoud M. ElBorai, Wagdy G. ElSayed, Mai Taha","doi":"10.3390/fractalfract7110796","DOIUrl":"https://doi.org/10.3390/fractalfract7110796","url":null,"abstract":"This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Color Image-Encryption Algorithm Using Extended DNA Coding and Zig-Zag Transform Based on a Fractional-Order Laser System 基于分数阶激光系统的扩展DNA编码和z形变换彩色图像加密算法

2区数学

Fractal and Fractional Pub Date : 2023-10-31 DOI: 10.3390/fractalfract7110795

Fanqi Meng, Zhenglan Gu

{"title":"A Color Image-Encryption Algorithm Using Extended DNA Coding and Zig-Zag Transform Based on a Fractional-Order Laser System","authors":"Fanqi Meng, Zhenglan Gu","doi":"10.3390/fractalfract7110795","DOIUrl":"https://doi.org/10.3390/fractalfract7110795","url":null,"abstract":"With the advancement of information technology, the security of digital images has become increasingly important. To ensure the integrity of images, a novel color image-encryption algorithm based on extended DNA coding, Zig-Zag transform, and a fractional-order laser system is proposed in this paper. First, the dynamic characteristics of the fractional-order laser chaotic system (FLCS) were analyzed using a phase diagram and Lyapunov exponent spectra. The chaotic sequences generated by the system were used to design image-encryption algorithms. Second, a modified Zig-Zag confusing method was adopted to confuse the image. Finally, in the diffusion link, the DNA encoding scheme was extended to allow for a greater number of DNA encoding rules, increasing the randomness of the matrix and improving the security of the encryption scheme. The performance of the designed encryption algorithm is analyzed using key space, a histogram, information entropy, correlation coefficients, differential attack, and robustness analysis. The experimental results demonstrate that the algorithm can withstand multiple decryption methods and has strong encryption capability. The proposed novel color image-encryption scheme enables secure communication of digital images.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"67 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135872139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis and Applications of Some New Fractional Integral Inequalities 一些新的分数阶积分不等式的分析与应用

2区数学

Fractal and Fractional Pub Date : 2023-10-31 DOI: 10.3390/fractalfract7110797

Sofia Ramzan, Muhammad Uzair Awan, Silvestru Sever Dragomir, Bandar Bin-Mohsin, Muhammad Aslam Noor

引用次数: 0