Fractal and Fractional最新文献_第3页

Enhancing the Pitch-Rate Control Performance of an F-16 Aircraft Using Fractional-Order Direct-MRAC Adaptive Control 利用分数阶直接-MRAC 自适应控制提高 F-16 飞机的俯仰速率控制性能

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-06-05 DOI: 10.3390/fractalfract8060338

Gustavo E. Ceballos Benavides, M. Duarte-Mermoud, Marcos E. Orchard, Alfonso Ehijo

引用次数: 0

Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise 莱维噪声下霍乱流行病非线性随机模型的动力学特性

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-16 DOI: 10.3390/fractalfract8050293

Q. Ain, Anwarud Din, Xiaoli Qiang, Zheng Kou

{"title":"Dynamics for a Nonlinear Stochastic Cholera Epidemic Model under Lévy Noise","authors":"Q. Ain, Anwarud Din, Xiaoli Qiang, Zheng Kou","doi":"10.3390/fractalfract8050293","DOIUrl":"https://doi.org/10.3390/fractalfract8050293","url":null,"abstract":"In this study, we develop a comprehensive mathematical model to analyze the dynamics of epidemic cholera, characterized by acute diarrhea due to pathogen overabundance in the human body. The model is first developed from a deterministic point of view, and then it is modified to include the randomness by stochastic differential equations. The study selected Lévy noise above other well-known types of noise, emphasizing its importance in epidemic modeling. Besides presenting a biological justification for the stochastic system, we demonstrate that the equivalent deterministic model exhibits possible equilibria. The introduction is followed by theoretical analysis of the model. Through rigorous analysis, we establish that the stochastic model ensures a unique global solution. Lyapunov function theory is applied to construct necessary conditions, which on average, guarantee the model’s stability for R0s>1. Our findings suggest the likelihood of eradicating the disease when Rs is below one, a significant insight supported by graphical simulations of the model. Graphical illustrations were generated from simulating the model in order to increase the analytical results’ robustness. This work provides a strong theoretical framework for a thorough comprehension of a range of such diseases. This research not only provides a deeper understanding of cholera dynamics but also offers a robust theoretical framework applicable to a range of similar diseases, alongside a novel approach for constructing Lyapunov functions for nonlinear models with random disturbances.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140967726","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

Critical Exponents and Universality for Fractal Time Processes above the Upper Critical Dimensionality 高临界维度以上分形时间过程的临界指数和普遍性

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-16 DOI: 10.3390/fractalfract8050294

Shaolong Zeng, Yangfan Hu, Shijing Tan, Biao Wang

引用次数: 0

Existence Results Related to a Singular Fractional Double-Phase Problem in the Whole Space 与全空间奇异分式双相问题有关的存在性结果

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-16 DOI: 10.3390/fractalfract8050292

R. Alsaedi

引用次数: 0

Distributed Control for Non-Cooperative Systems Governed by Time-Fractional Hyperbolic Operators 由时间分数双曲算子控制的非合作系统的分布式控制

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-16 DOI: 10.3390/fractalfract8050295

H. Serag, Areej A. Almoneef, Mahmoud El-Badawy, Abd-Allah Hyder

引用次数: 0

Exponential H∞ Output Control for Switching Fuzzy Systems via Event-Triggered Mechanism and Logarithmic Quantization 通过事件触发机制和对数量化实现开关模糊系统的指数 H∞ 输出控制

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-15 DOI: 10.3390/fractalfract8050290

Jiaojiao Ren, Can Zhao, Jianying Xiao, Renfu Luo, Nanrong He

引用次数: 0

Fractional-Order Dynamics in Epidemic Disease Modeling with Advanced Perspectives of Fractional Calculus 流行病建模中的分数阶动力学与分数微积分的高级视角

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-15 DOI: 10.3390/fractalfract8050291

Muhammad Riaz, Zareen A. Khan, Sadique Ahmad, A. Ateya

{"title":"Fractional-Order Dynamics in Epidemic Disease Modeling with Advanced Perspectives of Fractional Calculus","authors":"Muhammad Riaz, Zareen A. Khan, Sadique Ahmad, A. Ateya","doi":"10.3390/fractalfract8050291","DOIUrl":"https://doi.org/10.3390/fractalfract8050291","url":null,"abstract":"Piecewise fractional-order differential operators have received more attention in recent years because they can be used to describe various evolutionary dynamical problems to investigate crossover behaviors. In this manuscript, we use the aforementioned operators to investigate a mathematical model of COVID-19. By utilizing fractional calculus, our approach aims to capture the crossover dynamics of disease spread, considering heterogeneity and transitions between epidemic phases. This research seeks to develop a framework using specialized mathematical techniques, such as the Caputo fractional derivative, with the potential to investigate the crossover dynamical behaviors of the considered epidemic model. The anticipated contribution lies in bridging fractional calculus and epidemiology, offering insights for both theoretical advancements and practical public health interventions. In order to improve our understanding of epidemic dynamics and support, we used MATLAB to simulate numerical results for a visual representation of our findings. For this interpretation, we used various fractional-order values. In addition, we also compare our simulated results with some reported results for infected and death classes to demonstrate the efficiency of our numerical method.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973531","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

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces 巴纳赫空间中阶数 μ∈ (1, 2) 的 w 加权、Φ-Hilfer、非瞬时、脉冲、w 加权、分数、半线性微分结论的温和解决方案

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-13 DOI: 10.3390/fractalfract8050289

Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, M. M. Al-Sawalha, Khudhayr A. Rashedi

{"title":"Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces","authors":"Zainab Alsheekhhussain, Ahmed Gamal Ibrahim, M. M. Al-Sawalha, Khudhayr A. Rashedi","doi":"10.3390/fractalfract8050289","DOIUrl":"https://doi.org/10.3390/fractalfract8050289","url":null,"abstract":"The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140981942","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

Pore Fractal Characteristics between Marine and Marine–Continental Transitional Black Shales: A Case Study of Niutitang Formation and Longtan Formation 海相和海陆过渡黑页岩的孔隙分形特征：牛蹄塘地层和龙潭地层的案例研究

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-13 DOI: 10.3390/fractalfract8050288

Shitan Ning, Peng Xia, Fang Hao, Jinqiang Tian, Yong Fu, Ke Wang

{"title":"Pore Fractal Characteristics between Marine and Marine–Continental Transitional Black Shales: A Case Study of Niutitang Formation and Longtan Formation","authors":"Shitan Ning, Peng Xia, Fang Hao, Jinqiang Tian, Yong Fu, Ke Wang","doi":"10.3390/fractalfract8050288","DOIUrl":"https://doi.org/10.3390/fractalfract8050288","url":null,"abstract":"Marine shales from the Niutitang Formation and marine–continental transitional shales from the Longtan Formation are two sets of extremely important hydrocarbon source rocks in South China. In order to quantitatively compare the pore complexity characteristics between marine and marine–continental transitional shales, the shale and kerogen of the Niutitang Formation and the Longtan Formation are taken as our research subjects. Based on organic petrology, geochemistry, and low-temperature gas adsorption analyses, the fractal dimension of their pores is calculated by the Frenkel–Halsey–Hill (FHH) and Sierpinski models, and the influences of total organic carbon (TOC), vitrinite reflectance (Ro), and mineral composition on the pore fractals of the shale and kerogen are discussed. Our results show the following: (1) Marine shale predominantly has wedge-shaped and slit pores, while marine–continental transitional shale has inkpot-shaped and slit pores. (2) Cylindrical pores are common in organic matter of both shale types, with marine shale having a greater gas storage space (CRV) from organic matter pores, while marine–continental transitional shale relies more on inorganic pores, especially interlayer clay mineral pores, for gas storage due to their large specific surface area and high adsorption capacity (CRA). (3) The fractal characteristics of marine and marine–continental transitional shale pores are influenced differently. In marine shale, TOC positively correlates with fractal dimensions, while in marine–continental shale, Ro and clay minerals have a stronger influence. Ro is the primary factor affecting organic matter pore complexity. (4) Our two pore fractal models show that the complexity of the shale in the Longtan Formation surpasses that of the shale in the Niutitang Formation, and type I kerogen has more complex organic matter pores than type III, aiding in evaluating pore connectivity and flow effectiveness in shale reservoirs.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":5.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140984577","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

Time-Delay Effects on the Collective Resonant Behavior in Two Coupled Fractional Oscillators with Frequency Fluctuations 时间延迟对两个具有频率波动的耦合分数振荡器集体共振行为的影响

IF 5.4 2区数学

Fractal and Fractional Pub Date : 2024-05-11 DOI: 10.3390/fractalfract8050287

Minyue He, Huiqi Wang, Lifeng Lin

引用次数: 0