Fractal and Fractional最新文献_第9页

Semi-Analytical Solutions for Some Types of Nonlinear Fractional-Order Differential Equations Based on Third-Kind Chebyshev Polynomials 一类基于第三类Chebyshev多项式的非线性分数阶微分方程的半解析解

2区数学

Fractal and Fractional Pub Date : 2023-10-27 DOI: 10.3390/fractalfract7110784

Adel Abd Elaziz El-Sayed, Salah Boulaaras, Mohammed AbaOud

引用次数: 0

On Coefficient Inequalities of Starlike Functions Related to the q-Analog of Cosine Functions Defined by the Fractional q-Differential Operator 分数阶q-微分算子定义余弦函数的q-类似星状函数的系数不等式

2区数学

Fractal and Fractional Pub Date : 2023-10-26 DOI: 10.3390/fractalfract7110782

Yusra Taj, Sarfraz Nawaz Malik, Adriana Cătaş, Jong-Suk Ro, Fairouz Tchier, Ferdous M. O. Tawfiq

引用次数: 1

Difference between Charge–Voltage Relations of Ordinary and Fractional Capacitors 普通电容器与分式电容器电荷电压关系的差异

2区数学

Fractal and Fractional Pub Date : 2023-10-26 DOI: 10.3390/fractalfract7110781

Marthins, Eirik Brenner, Holm, Sverre

引用次数: 0

Evolution Law of Shallow Water in Multi-Face Mining Based on Partition Characteristics of Catastrophe Theory 基于突变理论分区特征的多工作面开采浅水演化规律

2区数学

Fractal and Fractional Pub Date : 2023-10-26 DOI: 10.3390/fractalfract7110779

Yujiang Zhang, Bingyuan Cui, Yining Wang, Shuai Zhang, Guorui Feng, Zhengjun Zhang

{"title":"Evolution Law of Shallow Water in Multi-Face Mining Based on Partition Characteristics of Catastrophe Theory","authors":"Yujiang Zhang, Bingyuan Cui, Yining Wang, Shuai Zhang, Guorui Feng, Zhengjun Zhang","doi":"10.3390/fractalfract7110779","DOIUrl":"https://doi.org/10.3390/fractalfract7110779","url":null,"abstract":"It is of great significance for ecological environment protection to clarify the regional evolution characteristics of shallow water under the disturbance of multi-working face mining. In this paper, the catastrophe theory method, GIS spatial analysis function and FEFLOW numerical calculation method were comprehensively used to study the instability risk and evolution law of shallow water systems in the Zhuan Longwan Coal Mine. The results show that: the Zhuan Longwan Coal Mine is divided into five areas (small risk area, light risk area, middle risk area, heavy risk area and special risk area) based on catastrophe theory, among which the middle risk area has the largest area of 16,616,880 m2, and the special risk area has the smallest area of 1,769,488 m2. Based on the results of catastrophe zoning, the evolution law of shallow water under multi-surface disturbance in different zones is expounded. In the middle-risk area, the water level drop at measuring point 4 is the largest, which is 0.525 m, and the water level drop at measuring point 5 is the smallest, which is 0.116 m. The study aims to provide a basis for regional coal development planning and research on the method of water-retaining coal mining.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136382017","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: 2

Optimal Control for Neutral Stochastic Integrodifferential Equations with Infinite Delay Driven by Poisson Jumps and Rosenblatt Process 由泊松跳变和Rosenblatt过程驱动的无穷延迟中立型随机积分微分方程的最优控制

2区数学

Fractal and Fractional Pub Date : 2023-10-26 DOI: 10.3390/fractalfract7110783

Dimplekumar Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan

{"title":"Optimal Control for Neutral Stochastic Integrodifferential Equations with Infinite Delay Driven by Poisson Jumps and Rosenblatt Process","authors":"Dimplekumar Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan","doi":"10.3390/fractalfract7110783","DOIUrl":"https://doi.org/10.3390/fractalfract7110783","url":null,"abstract":"In this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memory-phase space, in which we define the advanced phase space for infinite delay for the stochastic process. First, we introduce conditions that ensure the existence and uniqueness of mild solutions using stochastic analysis theory, successive approximation, and Grimmer’s resolvent operator theory. Next, we prove exponential stability, which includes mean square exponential stability, and this especially includes the exponential stability of solutions and their maps. Following that, we discuss the existence requirements of an optimal pair of systems governed by stochastic partial integrodifferential equations with infinite delay. Then, we explore examples that illustrate the potential of the main result, mainly in the heat equation, filter system, traffic signal light systems, and the biological processes in the human body. We conclude with a numerical simulation of the system studied. This work is a unique combination of the theory with practical examples and a numerical simulation.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"25 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134906777","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 Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation 求解非线性分布阶分数阶Bagley-Torvik微分方程的谱配法

2区数学

Fractal and Fractional Pub Date : 2023-10-26 DOI: 10.3390/fractalfract7110780

Ahmed Z. Amin, Mohamed A. Abdelkawy, Emad Solouma, Ibrahim Al-Dayel

引用次数: 0

Fractal and Spectral Analysis of Seismicity in the Lai Chau Area (Vietnam) 越南莱洲地区地震活动性的分形和谱分析

2区数学

Fractal and Fractional Pub Date : 2023-10-25 DOI: 10.3390/fractalfract7110776

Luciano Telesca, Anh Tuan Thai, Dinh Trong Cao, Dinh Trieu Cao, Quoc Van Dinh, Xuan Bach Mai

{"title":"Fractal and Spectral Analysis of Seismicity in the Lai Chau Area (Vietnam)","authors":"Luciano Telesca, Anh Tuan Thai, Dinh Trong Cao, Dinh Trieu Cao, Quoc Van Dinh, Xuan Bach Mai","doi":"10.3390/fractalfract7110776","DOIUrl":"https://doi.org/10.3390/fractalfract7110776","url":null,"abstract":"The time dynamics of the instrumental seismicity recorded in the area of the Lai Chau reservoir (Vietnam) between 2015 and 2021 were analyzed in this study. The Gutenberg–Richter analysis of the frequency–magnitude distribution has revealed that the seismic catalog is complete for events with magnitudes larger or equal to 0.6. The fractal method of the Allan Factor applied to the series of the occurrence times suggests that the seismic series is characterized by time-clustering behavior with rather large degrees of clustering, as indicated by the value of the fractal exponent α≈0.55. The time-clustering of the time distribution of the earthquakes is also confirmed by a global coefficient of variation value of 1.9 for the interevent times. The application of the correlogram-based periodogram, which is a robust method used to estimate the power spectrum of short series, has revealed three main cycles with a significance level of p<0.01 (of 10 months, 1 year, and 2 years) in the monthly variation of the mean water level of the reservoir, and two main periodicities with a significance level of p<0.01 (at 6 months and 2 years) in the monthly number of earthquakes. By decomposing the monthly earthquake counts into intrinsic mode functions (IMFs) using the empirical decomposition method (EMD), we identified two IMFs characterized by cycles of 10 months and 2 years, significant at the 1% level, and one cycle of 1 year, significant at the 5% level. The cycles identified in these two IMFs are consistent with those detected in the water level, showing that, in a rigorously statistical manner, the seismic process occurring in the Lai Chau area might be triggered by the loading–unloading operational cycles of the reservoir.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"101 1-2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135168612","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

High-Order Chebyshev Pseudospectral Tempered Fractional Operational Matrices and Tempered Fractional Differential Problems 高阶Chebyshev伪谱回火分数阶运算矩阵与回火分数阶微分问题

2区数学

Fractal and Fractional Pub Date : 2023-10-25 DOI: 10.3390/fractalfract7110777

Amel El-Abed, Sayed A. Dahy, H. M. El-Hawary, Tarek Aboelenen, Alaa Fahim

{"title":"High-Order Chebyshev Pseudospectral Tempered Fractional Operational Matrices and Tempered Fractional Differential Problems","authors":"Amel El-Abed, Sayed A. Dahy, H. M. El-Hawary, Tarek Aboelenen, Alaa Fahim","doi":"10.3390/fractalfract7110777","DOIUrl":"https://doi.org/10.3390/fractalfract7110777","url":null,"abstract":"This paper focuses on presenting an accurate, stable, efficient, and fast pseudospectral method to solve tempered fractional differential equations (TFDEs) in both spatial and temporal dimensions. We employ the Chebyshev interpolating polynomial for g at Gauss–Lobatto (GL) points in the range [−1,1] and any identically shifted range. The proposed method carries with it a recast of the TFDE into integration formulas to take advantage of the adaptation of the integral operators, hence avoiding the ill-conditioning and reduction in the convergence rate of integer differential operators. Via various tempered fractional differential applications, the present technique shows many advantages; for instance, spectral accuracy, a much higher rate of running, fewer computational hurdles and programming, calculating the tempered-derivative/integral of fractional order, and its spectral accuracy in comparison with other competitive numerical schemes. The study includes stability and convergence analyses and the elapsed times taken to construct the collocation matrices and obtain the numerical solutions, as well as a numerical examination of the produced condition number κ(A) of the resulting linear systems. The accuracy and efficiency of the proposed method are studied from the standpoint of the L2 and L∞-norms error and the fast rate of spectral convergence.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"9 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135216556","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

Fixed-Time Fractional-Order Sliding Mode Control for UAVs under External Disturbances 外部干扰下无人机的定时分数阶滑模控制

2区数学

Fractal and Fractional Pub Date : 2023-10-25 DOI: 10.3390/fractalfract7110775

Abdellah Benaddy, Moussa Labbadi, Kamal Elyaalaoui, Mostafa Bouzi

引用次数: 1

Multiple Terms Identification of Time Fractional Diffusion Equation with Symmetric Potential from Nonlocal Observation 基于非局部观测的对称势时间分数扩散方程的多项辨识

2区数学

Fractal and Fractional Pub Date : 2023-10-25 DOI: 10.3390/fractalfract7110778

Zewen Wang, Zhonglong Qiu, Shufang Qiu, Zhousheng Ruan

引用次数: 0