Fractal and Fractional最新文献_第10页

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties 具有指数拉波特诺夫核的双温分数 DPL 热弹性模型适用于特性可变的柔性圆柱体

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-22 DOI: 10.3390/fractalfract8040182

A. Abouelregal, Yazeed Alhassan, Hashem Althagafi, Faisal Alsharif

{"title":"A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties","authors":"A. Abouelregal, Yazeed Alhassan, Hashem Althagafi, Faisal Alsharif","doi":"10.3390/fractalfract8040182","DOIUrl":"https://doi.org/10.3390/fractalfract8040182","url":null,"abstract":"This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140220044","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

Adaptive Fractional-Order Multi-Scale Optimization TV-L1 Optical Flow Algorithm 自适应分阶多尺度优化 TV-L1 光流算法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-22 DOI: 10.3390/fractalfract8040179

Qi Yang, Yilu Wang, Lu Liu, Xiaomeng Zhang

引用次数: 0

Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System 广田时空分形耦合系统的研究

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-21 DOI: 10.3390/fractalfract8030178

Obaid J. Algahtani

{"title":"Investigation of a Spatio-Temporal Fractal Fractional Coupled Hirota System","authors":"Obaid J. Algahtani","doi":"10.3390/fractalfract8030178","DOIUrl":"https://doi.org/10.3390/fractalfract8030178","url":null,"abstract":"This article aims to examine the nonlinear excitations in a coupled Hirota system described by the fractal fractional order derivative. By using the Laplace transform with Adomian decomposition (LADM), the numerical solution for the considered system is derived. It has been shown that the suggested technique offers a systematic and effective method to solve complex nonlinear systems. Employing the Banach contraction theorem, it is confirmed that the LADM leads to a convergent solution. The numerical analysis of the solutions demonstrates the confinement of the carrier wave and the presence of confined wave packets. The dispersion nonlinear parameter reduction equally influences the wave amplitude and spatial width. The localized internal oscillations in the solitary waves decreased the wave collapsing effect at comparatively small dispersion. Furthermore, it is also shown that the amplitude of the solitary wave solution increases by reducing the fractal derivative. It is evident that decreasing the order α modifies the nature of the solitary wave solutions and marginally decreases the amplitude. The numerical and approximation solutions correspond effectively for specific values of time (t). However, when the fractal or fractional derivative is set to one by increasing time, the wave amplitude increases. The absolute error analysis between the obtained series solutions and the accurate solutions are also presented.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140221089","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

The Soliton Solutions for Nonlocal Multi-Component Higher-Order Gerdjikov–Ivanov Equation via Riemann–Hilbert Problem 通过黎曼-希尔伯特问题求非局部多分量高阶格尔吉科夫-伊万诺夫方程的孤子解

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-19 DOI: 10.3390/fractalfract8030177

Jinshan Liu, Huanhe Dong, Yong Fang, Yong Zhang

引用次数: 0

High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination 晶粒定向磁性钢层压中磁损耗的高频分数预测和空间分布

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-19 DOI: 10.3390/fractalfract8030176

Benjamin Ducharne, H. Hamzehbahmani, Yanhui Gao, P. Fagan, G. Sebald

{"title":"High-Frequency Fractional Predictions and Spatial Distribution of the Magnetic Loss in a Grain-Oriented Magnetic Steel Lamination","authors":"Benjamin Ducharne, H. Hamzehbahmani, Yanhui Gao, P. Fagan, G. Sebald","doi":"10.3390/fractalfract8030176","DOIUrl":"https://doi.org/10.3390/fractalfract8030176","url":null,"abstract":"Grain-oriented silicon steel (GO FeSi) laminations are vital components for efficient energy conversion in electromagnetic devices. While traditionally optimized for power frequencies of 50/60 Hz, the pursuit of higher frequency operation (f ≥ 200 Hz) promises enhanced power density. This paper introduces a model for estimating GO FeSi laminations’ magnetic behavior under these elevated operational frequencies. The proposed model combines the Maxwell diffusion equation and a material law derived from a fractional differential equation, capturing the viscoelastic characteristics of the magnetization process. Remarkably, the model’s dynamical contribution, characterized by only two parameters, achieves a notable 4.8% Euclidean relative distance error across the frequency spectrum from 50 Hz to 1 kHz. The paper’s initial section offers an exhaustive description of the model, featuring comprehensive comparisons between simulated and measured data. Subsequently, a methodology is presented for the localized segregation of magnetic losses into three conventional categories: hysteresis, classical, and excess, delineated across various tested frequencies. Further leveraging the model’s predictive capabilities, the study extends to investigating the very high-frequency regime, elucidating the spatial distribution of loss contributions. The application of proportional–iterative learning control facilitates the model’s adaptation to standard characterization conditions, employing sinusoidal imposed flux density. The paper deliberates on the implications of GO FeSi behavior under extreme operational conditions, offering insights and reflections essential for understanding and optimizing magnetic core performance in high-frequency applications.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140228447","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

Structural Characterization of Toxoplasma gondii Brain Cysts in a Model of Reactivated Toxoplasmosis Using Computational Image Analysis 利用计算图像分析确定再活化弓形虫病模型中弓形虫脑囊肿的结构特征

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-18 DOI: 10.3390/fractalfract8030175

N. Bauman, J. Srbljanović, Ivana Čolović Čalovski, Olivera Lijeskić, V. Ćirković, Jelena Trajković, B. Bobić, Andjelija Ž. Ilić, T. Štajner

{"title":"Structural Characterization of Toxoplasma gondii Brain Cysts in a Model of Reactivated Toxoplasmosis Using Computational Image Analysis","authors":"N. Bauman, J. Srbljanović, Ivana Čolović Čalovski, Olivera Lijeskić, V. Ćirković, Jelena Trajković, B. Bobić, Andjelija Ž. Ilić, T. Štajner","doi":"10.3390/fractalfract8030175","DOIUrl":"https://doi.org/10.3390/fractalfract8030175","url":null,"abstract":"Toxoplasma gondii is an obligate intracellular parasite existing in three infectious life stages—tachyzoites, bradyzoites, and sporozoites. Rupture of tissue cysts and re-conversion of bradyzoites to tachyzoites leads to reactivated toxoplasmosis (RT) in an immunocompromised host. The aim of this study was to apply ImageJ software for analysis of T. gondii brain cysts obtained from a newly established in vivo model of RT. Mice chronically infected with T. gondii (BGD1 and BGD26 strains) were treated with cyclophosphamide and hydrocortisone (experimental group—EG) or left untreated as infection controls (ICs). RT in mice was confirmed by qPCR (PCR+); mice remaining chronically infected were PCR−. A total of 90 images of cysts were analyzed for fractal dimension (FD), lacunarity (L), diameter (D), circularity (C), and packing density (PD). Circularity was significantly higher in PCR+ compared to IC mice (p < 0.05 for BGD1, p < 0.001 for the BGD26 strain). A significant negative correlation between D and PD was observed only in IC for the BGD1 strain (ρ = −0.384, p = 0.048), while fractal parameters were stable. Significantly higher D, C, and PD and lower lacunarity, L, were noticed in the BGD1 compared to the more aggressive BGD26 strain. In conclusion, these results demonstrate the complexity of structural alterations of T. gondii cysts in an immunocompromised host and emphasize the application potential of ImageJ in the experimental models of toxoplasmosis.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140231602","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

Quasi-P-Wave Reverse Time Migration in TTI Media with a Generalized Fractional Convolution Stencil 使用广义分数卷积模板的 TTI 介质中的准 P 波逆时迁移

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-18 DOI: 10.3390/fractalfract8030174

Shanyuan Qin, Jidong Yang, Ning Qin, Jianping Huang, Kun Tian

{"title":"Quasi-P-Wave Reverse Time Migration in TTI Media with a Generalized Fractional Convolution Stencil","authors":"Shanyuan Qin, Jidong Yang, Ning Qin, Jianping Huang, Kun Tian","doi":"10.3390/fractalfract8030174","DOIUrl":"https://doi.org/10.3390/fractalfract8030174","url":null,"abstract":"In seismic modeling and reverse time migration (RTM), incorporating anisotropy is crucial for accurate wavefield modeling and high-quality images. Due to the trade-off between computational cost and simulation accuracy, the pure quasi-P-wave equation has good accuracy to describe wave propagation in tilted transverse isotropic (TTI) media. However, it involves a fractional pseudo-differential operator that depends on the anisotropy parameters, making it unsuitable for resolution using conventional solvers for fractional operators. To address this issue, we propose a novel pure quasi-P-wave equation with a generalized fractional convolution operator in TTI media. First, we decompose the conventional pure quasi-P-wave equation into an elliptical anisotropy equation and a fractional pseudo-differential correction term. Then, we use a generalized fractional convolution stencil to approximate the spatial-domain pseudo-differential term through the solution of an inverse problem. The proposed approximation method is accurate, and the wavefield modeling method based on it also accurately describes quasi-P-wave propagation in TTI media. Moreover, it only increases the computational cost for calculating mixed partial derivatives compared to those in vertical transverse isotropic (VTI) media. Finally, the proposed wavefield modeling method is utilized in RTM to correct the anisotropic effects in seismic imaging. Numerical RTM experiments demonstrate the flexibility and viability of the proposed method.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140231553","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

Monotone Positive Radial Solution of Double Index Logarithm Parabolic Equations 双指数对数抛物方程的单调正径向解法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-16 DOI: 10.3390/fractalfract8030173

Mengru Liu, Lihong Zhang

引用次数: 0

Fractional Fuzzy Neural System: Fractional Differential-Based Compensation Prediction for Reputation Infringement Cases 分数模糊神经系统：基于分数差分的名誉侵权案件赔偿预测

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-16 DOI: 10.3390/fractalfract8030172

Ni Zhang, Wu-Yang Zhu, Peng Jin, Guo Huang, Yi-Fei Pu

{"title":"Fractional Fuzzy Neural System: Fractional Differential-Based Compensation Prediction for Reputation Infringement Cases","authors":"Ni Zhang, Wu-Yang Zhu, Peng Jin, Guo Huang, Yi-Fei Pu","doi":"10.3390/fractalfract8030172","DOIUrl":"https://doi.org/10.3390/fractalfract8030172","url":null,"abstract":"With the rise of social media and the internet, the rapid dissemination of information has increased the likelihood of reputation infringement. This study utilizes judicial big data and AI to analyze intrinsic connections in reputation infringement cases, aiding judges in delivering consistent rulings. The challenge lies in balancing freedom of speech with the right to reputation and addressing the ambiguity and subjectivity in infringement cases. This research constructs a structured reputation infringement case dataset from Chinese Judgments Online. It introduces a Fractional Fuzzy Neural System (FFNS) to tackle the vagueness in reputation infringement acts and judicial language, enhancing prediction accuracy for case outcomes. The FFNS, integrating fractional calculus, fuzzy logic, and neural networks, excels in adaptability and nonlinear modeling. It uses fractional order fuzzy membership functions to depict the extent and severity of reputation infringement accurately, combining these outputs with neural networks for predictive analysis. The result is a more precise adjudication tool, demonstrating significant potential for judicial application.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140236406","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

Identification of the Dynamic Trade Relationship between China and the United States Using the Quantile Grey Lotka–Volterra Model 利用量子灰色洛特卡-沃尔特拉模型识别中美动态贸易关系

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-03-15 DOI: 10.3390/fractalfract8030171

Zheng-Xin Wang, Yue-Ting Li, Ling-Fei Gao

引用次数: 0