Fractal and Fractional最新文献

Fractional-Order Total Variation Geiger-Mode Avalanche Photodiode Lidar Range-Image Denoising Algorithm Based on Spatial Kernel Function and Range Kernel Function 基于空间核函数和距离核函数的分数阶全变分盖格模式雪崩光电二极管激光雷达距离图像去噪算法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-07 DOI: 10.3390/fractalfract7090674

Xuyang Wei, Chunyang Wang, Da Xie, Kai Yuan, Xuelian Liu, Zihao Wang, Xinjian Wang, Tingsheng Huang

{"title":"Fractional-Order Total Variation Geiger-Mode Avalanche Photodiode Lidar Range-Image Denoising Algorithm Based on Spatial Kernel Function and Range Kernel Function","authors":"Xuyang Wei, Chunyang Wang, Da Xie, Kai Yuan, Xuelian Liu, Zihao Wang, Xinjian Wang, Tingsheng Huang","doi":"10.3390/fractalfract7090674","DOIUrl":"https://doi.org/10.3390/fractalfract7090674","url":null,"abstract":"A Geiger-mode avalanche photodiode (GM-APD) laser radar range image has much noise when the signal-to-background ratios (SBRs) are low, making it difficult to recover the real target scene. In this paper, based on the GM-APD lidar denoising model of fractional-order total variation (FOTV), the spatial relationship and similarity relationship between pixels are obtained by using a spatial kernel function and range kernel function to optimize the fractional differential operator, and a new FOTV GM-APD lidar range-image denoising algorithm is designed. The lost information and range anomalous noise are suppressed while the target details and contour information are preserved. The Monte Carlo simulation and experimental results show that, under the same SBRs and statistical frame number, the proposed algorithm improves the target restoration degree by at least 5.11% and the peak signal-to-noise ratio (PSNR) by at least 24.6%. The proposed approach can accomplish the denoising of GM-APD lidar range images when SBRs are low.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45482274","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

Fractal Characterization of Multiscale Fracture Network Distribution in Dolomites: Outcrop Analogue of Subsurface Reservoirs 白云岩多尺度裂缝网络分布的分形表征:地下储层露头模拟

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-07 DOI: 10.3390/fractalfract7090676

Ivica Pavičić, Ž. Duić, Anja Vrbaški, Ivan Dragičević

{"title":"Fractal Characterization of Multiscale Fracture Network Distribution in Dolomites: Outcrop Analogue of Subsurface Reservoirs","authors":"Ivica Pavičić, Ž. Duić, Anja Vrbaški, Ivan Dragičević","doi":"10.3390/fractalfract7090676","DOIUrl":"https://doi.org/10.3390/fractalfract7090676","url":null,"abstract":"Fractured aquifers, especially dolomites, are important hydrocarbon reservoirs and sources of thermal and groundwater in many parts of the world, especially in the Alpine-Dinaric-Carpathian region. The most dominant porosity type is fracture porosity, which acts as the preferential fluid pathway in the subsurface, thus strongly controlling fluid flow. Outcrops provide valuable information for the characterization of fracture networks. Dolomite rock properties and structural and diagenetic processes result in fractured systems that can be considered fractals. The fracture network was analyzed on 14 vertical outcrops in 35 digitized photographs. The values of the fractal dimensions varied slightly by the software and method used, but the trends were consistent, which confirms that all methods are valid. Small values of fractal dimension indicate the dominance of a few small or large fractures, and high values of fractal dimension result from a combination of large numbers of small fractures accompanied by a few large fractures. The mean value of the fractal dimension for analyzed fracture networks was 1.648. The results indicate that the fracture network of the Upper Triassic dolomites can be approximated by fractal distribution and can be considered a natural fractal, and values can be extrapolated to higher and lower scales (1D and 3D).","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41912940","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

Coefficient Inequalities of q-Bi-Univalent Mappings Associated with q-Hyperbolic Tangent Function 与q-双曲正切函数相关的q-二元映射的系数不等式

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-07 DOI: 10.3390/fractalfract7090675

T. G. Shaba, S. Araci, Jong-Suk Ro, F. Tchier, B. O. Adebesin, Saira Zainab

引用次数: 0

A New Hybrid Optimal Auxiliary Function Method for Approximate Solutions of Non-Linear Fractional Partial Differential Equations 非线性分数阶偏微分方程近似解的一种新的混合最优辅助函数方法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-07 DOI: 10.3390/fractalfract7090673

Rashid Ashraf, Rashid Nawaz, Osama Alabdali, Nicholas Fewster-Young, Ali Hasan Ali, Firas Ghanim, A. Alb Lupaș

{"title":"A New Hybrid Optimal Auxiliary Function Method for Approximate Solutions of Non-Linear Fractional Partial Differential Equations","authors":"Rashid Ashraf, Rashid Nawaz, Osama Alabdali, Nicholas Fewster-Young, Ali Hasan Ali, Firas Ghanim, A. Alb Lupaș","doi":"10.3390/fractalfract7090673","DOIUrl":"https://doi.org/10.3390/fractalfract7090673","url":null,"abstract":"This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and the Caputo derivative. This approach eliminates the need for assumptions about parameter magnitudes, offering a significant advantage. We validate our approach using the time-fractional Cahn–Hilliard, fractional Burgers–Poisson, and Benjamin–Bona–Mahony–Burger equations. Comparative testing shows that our method outperforms new iterative, homotopy perturbation, homotopy analysis, and residual power series methods. These examples highlight our method’s effectiveness in obtaining precise solutions for non-linear fractional differential equations, showcasing its superiority in accuracy and consistency. We underscore its potential for revealing elusive exact solutions by demonstrating success across various examples. Our methodology advances fractional differential equation research and equips practitioners with a tool for solving non-linear equations. A key feature is its ability to avoid parameter assumptions, enhancing its applicability to a broader range of problems and expanding the scope of problems addressable using fractional calculus techniques.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46812486","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: 1

Distribution and Fractal Characteristics of Outdoor Particles in High-Rise Buildings Based on Fractal Theory 基于分形理论的高层建筑室外颗粒物分布及分形特征

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-05 DOI: 10.3390/fractalfract7090669

Fuquan Liu, Tao Yu, Wenjun Leng, Xin Zhang

{"title":"Distribution and Fractal Characteristics of Outdoor Particles in High-Rise Buildings Based on Fractal Theory","authors":"Fuquan Liu, Tao Yu, Wenjun Leng, Xin Zhang","doi":"10.3390/fractalfract7090669","DOIUrl":"https://doi.org/10.3390/fractalfract7090669","url":null,"abstract":"It is of great significance to understand the particle distribution characteristics at different heights to effectively control particle pollution. Based on fractal theory, the fractal dimension of outdoor particles in a high-rise building in Xi’an and its relationship with the concentration of particles with different particle sizes are discussed and analyzed in this paper. The results indicate that the atmosphere in Xi’an is mainly composed of fine particles and that the average proportion of particles ranging from 0 to 1.0 µm is approximately 99.885% of the total particulates. The fractal dimension of particles in the atmosphere at different heights ranges from 5.014 to 5.764, with an average fractal dimension of 5.456. In summer, the fractal dimension of the outdoor particles on the 17th floor was the largest, at 5.764. The fractal dimension in summer is relatively high, being 0.158 higher than that in winter on average. The larger the fractal dimension, the higher the proportion of fine particles. In addition, the fractal dimension can characterize the adsorption of toxic and harmful gases by particles well. It provides parameter support for understanding particle distribution and the effective control of atmospheric particles at different heights and application values.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46658473","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: 1

Advanced Mathematical Approaches in Psycholinguistic Data Analysis: A Methodological Insight 心理语言学数据分析中的高级数学方法:方法论见解

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-05 DOI: 10.3390/fractalfract7090670

Cecilia Castro, Víctor Leiva, M. Lourenço-Gomes, A. Amorim

{"title":"Advanced Mathematical Approaches in Psycholinguistic Data Analysis: A Methodological Insight","authors":"Cecilia Castro, Víctor Leiva, M. Lourenço-Gomes, A. Amorim","doi":"10.3390/fractalfract7090670","DOIUrl":"https://doi.org/10.3390/fractalfract7090670","url":null,"abstract":"In the evolving landscape of psycholinguistic research, this study addresses the inherent complexities of data through advanced analytical methodologies, including permutation tests, bootstrap confidence intervals, and fractile or quantile regression. The methodology and philosophy of our approach deeply resonate with fractal and fractional concepts. Responding to the skewed distributions of data, which are observed in metrics such as reading times, time-to-response, and time-to-submit, our analysis highlights the nuanced interplay between time-to-response and variables like lists, conditions, and plausibility. A particular focus is placed on the implausible sentence response times, showcasing the precision of our chosen methods. The study underscores the profound influence of individual variability, advocating for meticulous analytical rigor in handling intricate and complex datasets. Drawing inspiration from fractal and fractional mathematics, our findings emphasize the broader potential of sophisticated mathematical tools in contemporary research, setting a benchmark for future investigations in psycholinguistics and related disciplines.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44168573","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

An Accurate Approach to Simulate the Fractional Delay Differential Equations 一种精确模拟分数阶时滞微分方程的方法

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-05 DOI: 10.3390/fractalfract7090671

Mohamed Adel, M. Khader, Salman Algelany, Khaled Aldwoah

引用次数: 0

New Cascaded 1+PII2D/FOPID Load Frequency Controller for Modern Power Grids including Superconducting Magnetic Energy Storage and Renewable Energy 用于现代电网的新型级联1+PII2D/FOPID负载频率控制器，包括超导磁储能和可再生能源

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-05 DOI: 10.3390/fractalfract7090672

F. El-Sousy, M. Aly, Mohammed H. Alqahtani, Ali S. Aljumah, Sulaiman Z. Almutairi, Emad A. Mohamed

{"title":"New Cascaded 1+PII2D/FOPID Load Frequency Controller for Modern Power Grids including Superconducting Magnetic Energy Storage and Renewable Energy","authors":"F. El-Sousy, M. Aly, Mohammed H. Alqahtani, Ali S. Aljumah, Sulaiman Z. Almutairi, Emad A. Mohamed","doi":"10.3390/fractalfract7090672","DOIUrl":"https://doi.org/10.3390/fractalfract7090672","url":null,"abstract":"Having continuous decrease in inertia and being sensitive to load/generation variation are considered crucial challenging problems for modern power grids. The main cause of these problems is the increased penetration capacities of renewables. An unbalanced load with generation power largely affects grids’ frequency and voltage profiles. Load frequency control (LFC) mechanisms are extensively presented to solve these problems. In the literature, LFC methods are still lacking in dealing with system uncertainty, parameter variation, structure changes, and/or disturbance rejection. Therefore, this paper proposes an improved LFC methodology using the hybrid one plus proportional integral double-integral derivative (1+PII2D) cascaded with fractional order proportional-integral-derivative (FOPID), namely, the proposed 1+PII2D/FOPID controller. The contribution of superconducting magnetic energy storage devices (SMES) is considered in the proposed design, also considering hybrid high-voltage DC and AC transmission lines (hybrid HVDC/HVAC). An optimized design of proposed 1+PII2D/FOPID controller is proposed using a new application of the recently presented powerful artificial rabbits optimizers (ARO) algorithm. Various performance comparisons, system changes, parameter uncertainties, and load/generation profiles and changes are considered in the proposed case study. The results proved superior regulation of frequency using proposed 1+PII2D/FOPID control and the ARO optimum parameters.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44884910","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: 1

A New Optimized FOPIDA-FOIDN Controller for the Frequency Regulation of Hybrid Multi-Area Interconnected Microgrids 一种用于混合多区域互联微电网频率调节的新型优化FOPIDA-FOIDN控制器

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-04 DOI: 10.3390/fractalfract7090666

Nessma M. Ahmed, Mohamed Ebeed, G. Magdy, Khairy Sayed, S. Gamoura, A. M. Metwally, Alaa A. Mahmoud

{"title":"A New Optimized FOPIDA-FOIDN Controller for the Frequency Regulation of Hybrid Multi-Area Interconnected Microgrids","authors":"Nessma M. Ahmed, Mohamed Ebeed, G. Magdy, Khairy Sayed, S. Gamoura, A. M. Metwally, Alaa A. Mahmoud","doi":"10.3390/fractalfract7090666","DOIUrl":"https://doi.org/10.3390/fractalfract7090666","url":null,"abstract":"This paper proposes a combined feedback and feed-forward control system to support the frequency regulation of multi-area interconnected hybrid microgrids considering renewable energy sources (RESs). The proposed control system is based on a fractional-order proportional-integral-derivative-accelerated (FOPIDA) controller in the feed-forward direction and a fractional-order integral-derivative with a low-pass filter compensator (FOIDN) controller in the feedback direction, referred to as a FOPIDA-FOIDN controller. Moreover, the parameters of the proposed FOPIDA-FOIDN controller (i.e., twelve parameters in each area) are optimally tuned using a proposed hybrid of two metaheuristic optimization algorithms, i.e., hybrid artificial gorilla troops optimizer (AGTO) and equilibrium optimizer (EO), and this hybrid is referred to as HGTOEO. The robustness and reliability of the proposed control system are validated by evaluating its performance in comparison to that of other counterparts’ controllers utilized in the literature, such as PID, FOPID, and tilt integral derivative (TID) controller, under the different operating conditions of the studied system. Furthermore, the proficiency of the proposed HGTOEO algorithm is checked against other powerful optimizers, such as the genetic algorithm, Jaya algorithm, improved Jaya algorithm, multi-verse optimizer, and cost-effective multi-verse optimizer, to optimally design the PID controller for the load frequency control of the studied two-area interconnected microgrid. The MATLAB simulation results demonstrate the viability and dependability of the proposed FOPIDA-FOIDN controller based on the HGTOEO algorithm under a variety of load perturbations and random production of RESs.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41679535","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: 1

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems 求解二维空间分数阶扩散问题的分数阶微分正交的独特形状函数

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2023-09-04 DOI: 10.3390/fractalfract7090668

Abdelfattah Mustafa, O. Ragb, M. Salah, Reda S. Salama, M. Mohamed

{"title":"Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems","authors":"Abdelfattah Mustafa, O. Ragb, M. Salah, Reda S. Salama, M. Mohamed","doi":"10.3390/fractalfract7090668","DOIUrl":"https://doi.org/10.3390/fractalfract7090668","url":null,"abstract":"The aim of this study is to utilize a differential quadrature method with various kernels, such as Lagrange interpolation and discrete singular convolution, to tackle problems related to the Riesz fractional diffusion equation and the Riesz fractional advection–dispersion equation. The governing equation for convection and diffusion depends on both spatial and transient factors. By using the block marching technique, we transform these equations into an algebraic system using differential quadrature methods and the Caputo-type fractional operator. Next, we develop a MATLAB program that generates code capable of solving the fractional convection–diffusion equation in (1+2) dimensions for each shape function. Our goal is to ensure that our methods are reliable, accurate, efficient, and capable of convergence. To achieve this, we conduct two experiments, comparing the numerical and graphical results with both analytical and numerical solutions. Additionally, we evaluate the accuracy of our findings using the L∞ error. Our tests show that the differential quadrature method, which relies mainly on the discrete singular convolution shape function, is a highly effective numerical approach for fractional convective diffusion problems. It offers superior accuracy, faster convergence, and greater reliability than other techniques. Furthermore, we study the impact of fractional order derivatives, velocity, and positive diffusion parameters on the results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":" ","pages":""},"PeriodicalIF":5.4,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43940043","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