Fractal and Fractional最新文献_第3页

Fractional Photoconduction and Nonlinear Optical Behavior in ZnO Micro and Nanostructures 氧化锌微纳米结构中的分数光电导和非线性光学行为

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-15 DOI: 10.3390/fractalfract7120885

Victor Manuel Garcia-de-los-Rios, Jose Alberto Arano-Martínez, M. Trejo-Valdez, Martha Leticia Hernández-Pichardo, M. A. Vidales-Hurtado, C. Torres‐Torres

{"title":"Fractional Photoconduction and Nonlinear Optical Behavior in ZnO Micro and Nanostructures","authors":"Victor Manuel Garcia-de-los-Rios, Jose Alberto Arano-Martínez, M. Trejo-Valdez, Martha Leticia Hernández-Pichardo, M. A. Vidales-Hurtado, C. Torres‐Torres","doi":"10.3390/fractalfract7120885","DOIUrl":"https://doi.org/10.3390/fractalfract7120885","url":null,"abstract":"A fractional description for the optically induced mechanisms responsible for conductivity and multiphotonic effects in ZnO nanomaterials is studied here. Photoconductive, electrical, and nonlinear optical phenomena exhibited by pure micro and nanostructured ZnO samples were analyzed. A hydrothermal approach was used to synthetize ZnO micro-sized crystals, while a spray pyrolysis technique was employed to prepare ZnO nanostructures. A contrast in the fractional electrical behavior and photoconductivity was identified for the samples studied. A positive nonlinear refractive index was measured on the nanoscale sample using the z-scan technique, which endows it with a dominant real part for the third-order optical nonlinearity. The absence of nonlinear optical absorption, along with a strong optical Kerr effect in the ZnO nanostructures, shows favorable perspectives for their potential use in the development of all-optical switching devices. Fractional models for predicting electronic and nonlinear interactions in nanosystems could pave the way for the development of optoelectronic circuits and ultrafast functions controlled by ZnO photo technology.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"86 5","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138999545","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

Faber Polynomial Coefficient Inequalities for a Subclass of Bi-Close-To-Convex Functions Associated with Fractional Differential Operator 与分式微分算子相关的双近凸函数子类的法布尔多项式系数不等式

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-14 DOI: 10.3390/fractalfract7120883

F. Tawfiq, F. Tchier, Luminița-Ioana Cotîrlă

引用次数: 0

Some Results on Fractional Boundary Value Problem for Caputo-Hadamard Fractional Impulsive Integro Differential Equations 关于卡普托-哈达玛德分式脉冲积分微分方程的分式边界值问题的一些结果

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-14 DOI: 10.3390/fractalfract7120884

Y. Alruwaily, Kuppusamy Venkatachalam, El-sayed El-hady

引用次数: 0

Radial Basis Functions Approximation Method for Time-Fractional FitzHugh–Nagumo Equation 时分数 FitzHugh-Nagumo 方程的径向基函数逼近法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-13 DOI: 10.3390/fractalfract7120882

Mehboob Alam, S. Haq, Ihteram Ali, M. Ebadi, S. Salahshour

引用次数: 0

Novel Low-Pass Two-Dimensional Mittag–Leffler Filter and Its Application in Image Processing 新型低通二维 Mittag-Leffler 滤波器及其在图像处理中的应用

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-13 DOI: 10.3390/fractalfract7120881

Ivo Petráš

引用次数: 0

High-Accuracy Simulation of Rayleigh Waves Using Fractional Viscoelastic Wave Equation 利用分数粘弹性波方程高精度模拟瑞利波

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-12 DOI: 10.3390/fractalfract7120880

Yinfeng Wang, Jilong Lu, Ying Shi, Ning Wang, Liguo Han

{"title":"High-Accuracy Simulation of Rayleigh Waves Using Fractional Viscoelastic Wave Equation","authors":"Yinfeng Wang, Jilong Lu, Ying Shi, Ning Wang, Liguo Han","doi":"10.3390/fractalfract7120880","DOIUrl":"https://doi.org/10.3390/fractalfract7120880","url":null,"abstract":"The propagation of Rayleigh waves is usually accompanied by dispersion, which becomes more complex with inherent attenuation. The accurate simulation of Rayleigh waves in attenuation media is crucial for understanding wave mechanisms, layer thickness identification, and parameter inversion. Although the vacuum formalism or stress image method (SIM) combined with the generalized standard linear solid (GSLS) is widely used to implement the numerical simulation of Rayleigh waves in attenuation media, this type of method still has its limitations. First, the GSLS model cannot split the velocity dispersion and amplitude attenuation term, thus limiting its application in the Q-compensated reverse time migration/full waveform inversion. In addition, GSLS-model-based wave equation is usually numerically solved using staggered-grid finite-difference (SGFD) method, which may result in the numerical dispersion due to the harsh stability condition and poses complexity and computational burden. To overcome these issues, we propose a high-accuracy Rayleigh-waves simulation scheme that involves the integration of the fractional viscoelastic wave equation and vacuum formalism. The proposed scheme not only decouples the amplitude attenuation and velocity dispersion but also significantly suppresses the numerical dispersion of Rayleigh waves under the same grid sizes. We first use a homogeneous elastic model to demonstrate the accuracy in comparison with the analytical solutions, and the correctness for a viscoelastic half-space model is verified by comparing the phase velocities with the dispersive images generated by the phase shift transformation. We then simulate several two-dimensional synthetic models to analyze the effectiveness and applicability of the proposed method. The results show that the proposed method uses twice as many spatial step sizes and takes 0.6 times that of the GSLS method (solved by the SGFD method) when achieved at 95% accuracy.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"26 7","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139008824","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 Maclaurin-Type Inequalities for Multiplicatively Convex Functions 乘凸函数的分式麦克劳林不等式

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-12 DOI: 10.3390/fractalfract7120879

M. Merad, B. Meftah, Abdelkader Moumen, Mohamed Bouye

引用次数: 0

Improved Results on Delay-Dependent and Order-Dependent Criteria of Fractional-Order Neural Networks with Time Delay Based on Sampled-Data Control 基于采样数据控制的具有时延的分数阶神经网络的时延依赖性和阶次依赖性准则的改进结果

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-12-11 DOI: 10.3390/fractalfract7120876

Junzhou Dai, Lianglin Xiong, Haiyang Zhang, Weiguo Rui

引用次数: 0

On Constructing a Family of Sixth-Order Methods for Multiple Roots 论构建多根六阶方法族