Fractal and Fractional最新文献_第5页

Analytic Functions Related to a Balloon-Shaped Domain 与气球形域相关的解析函数

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-05 DOI: 10.3390/fractalfract7120865

Adeel Ahmad, Jianhua Gong, Isra Al-shbeil, A. Rasheed, Asad Ali, Saqib Hussain

引用次数: 0

Convergence Rate of the Diffused Split-Step Truncated Euler–Maruyama Method for Stochastic Pantograph Models with Lévy Leaps 有列维跃迁的随机受电弓模型的扩散分步截断欧拉-Maruyama 方法的收敛率

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-04 DOI: 10.3390/fractalfract7120861

Amr Abou-Senna, Ghada AlNemer, Yongchun Zhou, Boping Tian

引用次数: 0

Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults 具有传感器和执行器故障的不确定分数阶非线性系统的自适应模糊容错控制

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-04 DOI: 10.3390/fractalfract7120862

Ke Sun, Zhiyao Ma, Guowei Dong, Ping Gong

引用次数: 0

Maclaurin-Type Integral Inequalities for GA-Convex Functions Involving Confluent Hypergeometric Function via Hadamard Fractional Integrals 通过哈达玛分式积分求涉及汇合超几何函数的 GA-Convex 函数的 Maclaurin 型积分不等式

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-02 DOI: 10.3390/fractalfract7120860

T. Chiheb, B. Meftah, Abdelkader Moumen, Mohamed Bouye

引用次数: 0

An Algorithm for Crack Detection, Segmentation, and Fractal Dimension Estimation in Low-Light Environments by Fusing FFT and Convolutional Neural Network 融合FFT和卷积神经网络的弱光环境下裂纹检测、分割和分形维数估计算法

2区数学

Fractal and Fractional Pub Date : 2023-11-14 DOI: 10.3390/fractalfract7110820

Jiajie Cheng, Qiunan Chen, Xiaocheng Huang

{"title":"An Algorithm for Crack Detection, Segmentation, and Fractal Dimension Estimation in Low-Light Environments by Fusing FFT and Convolutional Neural Network","authors":"Jiajie Cheng, Qiunan Chen, Xiaocheng Huang","doi":"10.3390/fractalfract7110820","DOIUrl":"https://doi.org/10.3390/fractalfract7110820","url":null,"abstract":"The segmentation of crack detection and severity assessment in low-light environments presents a formidable challenge. To address this, we propose a novel dual encoder structure, denoted as DSD-Net, which integrates fast Fourier transform with a convolutional neural network. In this framework, we incorporate an information extraction module and an attention feature fusion module to effectively capture contextual global information and extract pertinent local features. Furthermore, we introduce a fractal dimension estimation method into the network, seamlessly integrated as an end-to-end task, augmenting the proficiency of professionals in detecting crack pathology within low-light settings. Subsequently, we curate a specialized dataset comprising instances of crack pathology in low-light conditions to facilitate the training and evaluation of the DSD-Net algorithm. Comparative experimentation attests to the commendable performance of DSD-Net in low-light environments, exhibiting superlative precision (88.5%), recall (85.3%), and F1 score (86.9%) in the detection task. Notably, DSD-Net exhibits a diminutive Model Size (35.3 MB) and elevated Frame Per Second (80.4 f/s), thereby endowing it with the potential to be seamlessly integrated into edge detection devices, thus amplifying its practical utility.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"54 34","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134902629","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

On Mixed Fractional Lifting Oscillation Spaces 关于混合分数阶提升振荡空间

2区数学

Fractal and Fractional Pub Date : 2023-11-13 DOI: 10.3390/fractalfract7110819

Imtithal Alzughaibi, Mourad Ben Slimane, Obaid Algahtani

{"title":"On Mixed Fractional Lifting Oscillation Spaces","authors":"Imtithal Alzughaibi, Mourad Ben Slimane, Obaid Algahtani","doi":"10.3390/fractalfract7110819","DOIUrl":"https://doi.org/10.3390/fractalfract7110819","url":null,"abstract":"We introduce hyperbolic oscillation spaces and mixed fractional lifting oscillation spaces expressed in terms of hyperbolic wavelet leaders of multivariate signals on Rd, with d≥2. Contrary to Besov spaces and fractional Sobolev spaces with dominating mixed smoothness, the new spaces take into account the geometric disposition of the hyperbolic wavelet coefficients at each scale (j1,⋯,jd), and are therefore suitable for a multifractal analysis of rectangular regularity. We prove that hyperbolic oscillation spaces are closely related to hyperbolic variation spaces, and consequently do not almost depend on the chosen hyperbolic wavelet basis. Therefore, the so-called rectangular multifractal analysis, related to hyperbolic oscillation spaces, is somehow ‘robust’, i.e., does not change if the analyzing wavelets were changed. We also study optimal relationships between hyperbolic and mixed fractional lifting oscillation spaces and Besov spaces with dominating mixed smoothness. In particular, we show that, for some indices, hyperbolic and mixed fractional lifting oscillation spaces are not always sharply imbedded between Besov spaces or fractional Sobolev spaces with dominating mixed smoothness, and thus are new spaces of a really different nature.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"140 41","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352190","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

Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network 一种新型小型异构耦合网络的相位同步与动态特性

2区数学

Fractal and Fractional Pub Date : 2023-11-13 DOI: 10.3390/fractalfract7110818

Mengjiao Wang, Jiwei Peng, Shaobo He, Xinan Zhang, Herbert Ho-Ching Iu

{"title":"Phase Synchronization and Dynamic Behavior of a Novel Small Heterogeneous Coupled Network","authors":"Mengjiao Wang, Jiwei Peng, Shaobo He, Xinan Zhang, Herbert Ho-Ching Iu","doi":"10.3390/fractalfract7110818","DOIUrl":"https://doi.org/10.3390/fractalfract7110818","url":null,"abstract":"Studying the firing dynamics and phase synchronization behavior of heterogeneous coupled networks helps us understand the mechanism of human brain activity. In this study, we propose a novel small heterogeneous coupled network in which the 2D Hopfield neural network (HNN) and the 2D Hindmarsh–Rose (HR) neuron are coupled through a locally active memristor. The simulation results show that the network exhibits complex dynamic behavior and is different from the usual phase synchronization. More specifically, the membrane potential of the 2D HR neuron exhibits five stable firing modes as the coupling parameter k1 changes. In addition, it is found that in the local region of k1, the number of spikes in bursting firing increases with the increase in k1. More interestingly, the network gradually changes from synchronous to asynchronous during the increase in the coupling parameter k1 but suddenly becomes synchronous around the coupling parameter k1 = 1.96. As far as we know, this abnormal synchronization behavior is different from the existing findings. This research is inspired by the fact that the episodic synchronous abnormal firing of excitatory neurons in the hippocampus of the brain can lead to diseases such as epilepsy. This helps us further understand the mechanism of brain activity and build bionic systems. Finally, we design the simulation circuit of the network and implement it on an STM32 microcontroller.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136347177","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

Solving a Nonlinear Fractional Differential Equation Using Fixed Point Results in Orthogonal Metric Spaces 利用正交度量空间中的不动点结果求解非线性分数阶微分方程

2区数学

Fractal and Fractional Pub Date : 2023-11-12 DOI: 10.3390/fractalfract7110817

Afrah Ahmad Noman Abdou

引用次数: 0

Systems of Hilfer–Hadamard Fractional Differential Equations with Nonlocal Coupled Boundary Conditions 具有非局部耦合边界条件的Hilfer-Hadamard分数阶微分方程组

2区数学

Fractal and Fractional Pub Date : 2023-11-11 DOI: 10.3390/fractalfract7110816

Alexandru Tudorache, Rodica Luca

引用次数: 0

Temporal Fractal Nature of the Time-Fractional SPIDEs and Their Gradient 时间分数型SPIDEs的分形性质及其梯度

2区数学

Fractal and Fractional Pub Date : 2023-11-11 DOI: 10.3390/fractalfract7110815

Wensheng Wang

{"title":"Temporal Fractal Nature of the Time-Fractional SPIDEs and Their Gradient","authors":"Wensheng Wang","doi":"10.3390/fractalfract7110815","DOIUrl":"https://doi.org/10.3390/fractalfract7110815","url":null,"abstract":"Fractional and high-order PDEs have become prominent in theory and in the modeling of many phenomena. In this article, we study the temporal fractal nature for fourth-order time-fractional stochastic partial integro-differential equations (TFSPIDEs) and their gradients, which are driven in one-to-three dimensional spaces by space–time white noise. By using the underlying explicit kernels, we prove the exact global temporal continuity moduli and temporal laws of the iterated logarithm for the TFSPIDEs and their gradients, as well as prove that the sets of temporal fast points (where the remarkable oscillation of the TFSPIDEs and their gradients happen infinitely often) are random fractals. In addition, we evaluate their Hausdorff dimensions and their hitting probabilities. It has been confirmed that these points of the TFSPIDEs and their gradients, in time, are most likely one everywhere, and are dense with the power of the continuum. Moreover, their hitting probabilities are determined by the target set B’s packing dimension dimp(B). On the one hand, this work reinforces the temporal moduli of the continuity and temporal LILs obtained in relevant literature, which were achieved by obtaining the exact values of their normalized constants; on the other hand, this work obtains the size of the set of fast points, as well as a potential theory of TFSPIDEs and their gradients.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"37 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135086594","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