Fractal and Fractional最新文献

Calculation of the Relaxation Modulus in the Andrade Model by Using the Laplace Transform 利用拉普拉斯变换计算安德拉德模型中的松弛模量

Fractal and Fractional Pub Date : 2024-07-26 DOI: 10.3390/fractalfract8080439

Juan Luis González-Santander, Giorgio Spada, Francesco Mainardi, Alexander Apelblat

引用次数: 0

Existence of Solutions for Caputo Sequential Fractional Differential Inclusions with Nonlocal Generalized Riemann–Liouville Boundary Conditions 具有非局部广义黎曼-刘维尔边界条件的卡普托序列分微分方程的解的存在性

Fractal and Fractional Pub Date : 2024-07-26 DOI: 10.3390/fractalfract8080441

M. Manigandan, Saravanan Shanmugam, Mohamed Rhaima, Elango Sekar

引用次数: 0

Morphological Features of Mathematical and Real-World Fractals: A Survey 数学和现实世界分形的形态特征：概览

Fractal and Fractional Pub Date : 2024-07-26 DOI: 10.3390/fractalfract8080440

M. Patiño-Ortiz, J. Patiño-Ortiz, M. Martínez-Cruz, Fernando René Esquivel-Patiño, A. Balankin

引用次数: 0

An Application of Multiple Erdélyi–Kober Fractional Integral Operators to Establish New Inequalities Involving a General Class of Functions 应用多重埃代利-科贝尔分式积分算子建立涉及一般函数类别的新不等式

Fractal and Fractional Pub Date : 2024-07-25 DOI: 10.3390/fractalfract8080438

Asifa Tassaddiq, R. Srivastava, Rabab Alharbi, R. Kasmani, Sania Qureshi

引用次数: 0

Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading 循环冲击载荷下红色砂岩孔隙结构和分形特征的演变

Fractal and Fractional Pub Date : 2024-07-24 DOI: 10.3390/fractalfract8080437

Huanhuan Qiao, Peng Wang, Zhen Jiang, Yao Liu, Guanglin Tian, Bokun Zhao

{"title":"Evolution of Pore Structure and Fractal Characteristics in Red Sandstone under Cyclic Impact Loading","authors":"Huanhuan Qiao, Peng Wang, Zhen Jiang, Yao Liu, Guanglin Tian, Bokun Zhao","doi":"10.3390/fractalfract8080437","DOIUrl":"https://doi.org/10.3390/fractalfract8080437","url":null,"abstract":"Fatigue damage can occur in surface rock engineering due to various factors, including earthquakes, blasting, and impacts. The underlying cause for the variations in physical and mechanical properties of the rock resulting from impact loading is the alteration in the internal pore structure. To investigate the evolution characteristics of the pore structure under impact fatigue damage, red sandstone subjected to cyclic impact compression by split Hopkinson pressure bar (SHPB) was analyzed using nuclear magnetic resonance (NMR) technology. The parameters describing the evolution of pore structure were obtained and quantified using fractal methods. The development of the pore structure in rocks subjected to cyclic impact was quantitatively analyzed, and two fractal evolution models based on pore size and pore connectivity were constructed. The results indicate that with an increasing number of impact loading cycles, the porosity of the red sandstone gradually increases, the T2 cutoff (T2c) value decreases, the most probable gray value of magnetic resonance imaging (MRI) increases, the pores’ connectivity is enhanced, and the fractal dimension decreases gradually. Moreover, the pore distribution space tends to transition from three-dimensional to two-dimensional, suggesting the expansion of dominant pores into clusters, forming microfractures or even macroscopic fissures. The findings provide valuable insights into the impact fatigue characteristics of rocks from a microscopic perspective and contribute to the evaluation of time-varying stability and the assessment of progressive damage in rock engineering.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"38 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141809430","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

Semi-Regular Continued Fractions with Fast-Growing Partial Quotients 具有快速增长部分商的半整式连续分数

Fractal and Fractional Pub Date : 2024-07-24 DOI: 10.3390/fractalfract8080436

Sh. Kadyrov, A. Kazin, F. Mashurov

引用次数: 0

Analytic Solution of the Time-Fractional Partial Differential Equation Using a Multi-G-Laplace Transform Method 用多G-拉普拉斯变换法解析时分数偏微分方程

Fractal and Fractional Pub Date : 2024-07-23 DOI: 10.3390/fractalfract8080435

Hassan Eltayeb

引用次数: 0

A Stable Forward Modeling Approach in Heterogeneous Attenuating Media Using Reapplied Hilbert Transform 使用重应用希尔伯特变换的异质衰减介质稳定前向建模方法

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070434

Songmei Deng, Shaolin Shi, Hongwei Liu

{"title":"A Stable Forward Modeling Approach in Heterogeneous Attenuating Media Using Reapplied Hilbert Transform","authors":"Songmei Deng, Shaolin Shi, Hongwei Liu","doi":"10.3390/fractalfract8070434","DOIUrl":"https://doi.org/10.3390/fractalfract8070434","url":null,"abstract":"In the field of geological exploration and wave propagation theory, particularly in heterogeneous attenuating media, the stability of numerical simulations is a significant challenge for implementing effective attenuation compensation strategies. Consequently, the development and optimization of algorithms and techniques that can mitigate these numerical instabilities are critical for ensuring the accuracy and practicality of attenuation compensation methods. This is essential to reveal subsurface structure information accurately and enhance the reliability of geological interpretation. We present a method for stable forward modeling in strongly attenuating media by reapplying the Hilbert transform to eliminate increasing negative frequency components. We derived and validated new constant-Q wave equation (CWE) formulations and a stable solving method. Our study reveals that the original CWE equations, when utilizing the analytic signal, regenerate and amplify negative frequencies, leading to instability. Implementing our method maintains high accuracy between analytical and numerical solutions. The application of our approach to the Chimney Model, compared with results from the acoustic wave equation, confirms the reliability and effectiveness of the proposed equations and method.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"17 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141816321","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

Numerical Performance of the Fractional Direct Spreading Cholera Disease Model: An Artificial Neural Network Approach 分式直接传播霍乱疾病模型的数值性能：人工神经网络方法

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070432

Saadia Malik

{"title":"Numerical Performance of the Fractional Direct Spreading Cholera Disease Model: An Artificial Neural Network Approach","authors":"Saadia Malik","doi":"10.3390/fractalfract8070432","DOIUrl":"https://doi.org/10.3390/fractalfract8070432","url":null,"abstract":"The current investigation examines the numerical performance of the fractional-order endemic disease model based on the direct spreading of cholera by applying the neuro-computing Bayesian regularization (BR) neural network process. The purpose is to present the numerical solutions of the fractional-order model, which provides more precise solutions as compared to the integer-order one. Real values based on the parameters can be obtained and one can achieve better results by utilizing these values. The mathematical form of the fractional direct spreading cholera disease is categorized as susceptible, infected, treatment, and recovered, which represents a nonlinear model. The construction of the dataset is performed through the implicit Runge–Kutta method, which is used to lessen the mean square error by taking 74% of the data for training, while 8% is used for both validation and testing. Twenty-two neurons and the log-sigmoid fitness function in the hidden layer are used in the stochastic neural network process. The optimization of BR is performed in order to solve the direct spreading cholera disease problem. The accuracy of the stochastic process is authenticated through the valuation of the outputs, whereas the negligible calculated absolute error values demonstrate the approach’s correctness. Furthermore, the statistical operator performance establishes the reliability of the proposed scheme.","PeriodicalId":510138,"journal":{"name":"Fractal and Fractional","volume":"28 41","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814489","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

Securing Bipartite Nonlinear Fractional-Order Multi-Agent Systems against False Data Injection Attacks (FDIAs) Considering Hostile Environment 考虑到敌对环境，确保双部分非线性分数阶多代理系统免受虚假数据注入攻击（FDIAs）的安全

Fractal and Fractional Pub Date : 2024-07-22 DOI: 10.3390/fractalfract8070430

Hanen Louati, Saadia Rehman, Farhat Imtiaz, Nafisa A. Albasheir, A. Y. Al-Rezami, Mohammed M. A. Almazah, A. U. K. Niazi

引用次数: 0