Fractal and Fractional最新文献_第8页

The Iterative Properties for Positive Solutions of a Tempered Fractional Equation 缓变分数阶方程正解的迭代性质

2区数学

Fractal and Fractional Pub Date : 2023-10-16 DOI: 10.3390/fractalfract7100761

Xinguang Zhang, Peng Chen, Hui Tian, Yonghong Wu

引用次数: 0

A Fractional-Order Fidelity-Based Total Generalized Variation Model for Image Deblurring 基于分数阶保真度的图像去模糊全广义变分模型

2区数学

Fractal and Fractional Pub Date : 2023-10-13 DOI: 10.3390/fractalfract7100756

Juanjuan Gao, Jiebao Sun, Zhichang Guo, Wenjuan Yao

引用次数: 0

An H1-Galerkin Space-Time Mixed Finite Element Method for Semilinear Convection–Diffusion–Reaction Equations 半线性对流-扩散-反应方程的H1-Galerkin时空混合有限元法

2区数学

Fractal and Fractional Pub Date : 2023-10-13 DOI: 10.3390/fractalfract7100757

Xuehui Ren, Siriguleng He, Hong Li

引用次数: 0

Operator Kernel Functions in Operational Calculus and Applications in Fractals with Fractional Operators 运算微积分中的算子核函数及其在分形中的应用

2区数学

Fractal and Fractional Pub Date : 2023-10-13 DOI: 10.3390/fractalfract7100755

Xiaobin Yu, Yajun Yin

{"title":"Operator Kernel Functions in Operational Calculus and Applications in Fractals with Fractional Operators","authors":"Xiaobin Yu, Yajun Yin","doi":"10.3390/fractalfract7100755","DOIUrl":"https://doi.org/10.3390/fractalfract7100755","url":null,"abstract":"In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation operator e−pt, which bears a striking resemblance to the Laplace transform. Our research demonstrates the uniqueness of the kernel function, determined by the rules of operational calculus and its integral representation. This discovery provides a novel perspective on how the operational calculus can be understood and applied, particularly through convolution with kernel functions. We substantiate the accuracy of the proposed method by demonstrating the consistency between the operator solution and the classical solution for the heat conduction problem. Subsequently, on the fractal tree, fractal loop, and fractal ladder structures, we illustrate the application of operational calculus in viscoelastic constitutive and hemodynamics confirming that the method proposed unifies the OKFs in the existing OC theory and can be extended to the operator field. These results underscore the practical significance of our results and open up new possibilities for future research.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135855641","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

Stochastic Modeling of Three-Species Prey–Predator Model Driven by Lévy Jump with Mixed Holling-II and Beddington–DeAngelis Functional Responses 具有Holling-II和Beddington-DeAngelis混合功能响应的lsamvy跳跃驱动的三物种捕食-捕食模型的随机建模

2区数学

Fractal and Fractional Pub Date : 2023-10-12 DOI: 10.3390/fractalfract7100751

Jaouad Danane, Mehmet Yavuz, Mustafa Yıldız

引用次数: 0

To the Theory of Decaying Turbulence 到衰减湍流理论

2区数学

Fractal and Fractional Pub Date : 2023-10-12 DOI: 10.3390/fractalfract7100754

Alexander Migdal

{"title":"To the Theory of Decaying Turbulence","authors":"Alexander Migdal","doi":"10.3390/fractalfract7100754","DOIUrl":"https://doi.org/10.3390/fractalfract7100754","url":null,"abstract":"We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension d>2. This solution family is equivalent to a fractal curve in complex space Cd with random steps parametrized by N Ising variables σi=±1, in addition to a rational number pq and an integer winding number r, related by ∑σi=qr. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in Rd space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size N→∞ or its chemical potential μ→0. The system with fixed N has different asymptotics at odd and even N→∞, but the limit μ→0 is well defined. The energy dissipation rate is analytically calculated as a function of μ using methods of number theory. It grows as ν/μ2 in the continuum limit μ→0, leading to anomalous dissipation at μ∝ν→0. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as t−λ, with a continuous spectrum of indexes λ in the local limit μ→0. The spectrum is determined by a resolvent, which is represented as an infinite product of 3⊗3 matrices depending of the element of the Euler ensemble.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"294 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135968355","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

Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation 随机分数阶Kuramoto-Sivashinsky方程中奇异随机孤子的动力学解

2区数学

Fractal and Fractional Pub Date : 2023-10-12 DOI: 10.3390/fractalfract7100753

M. Mossa Al-Sawalha, Humaira Yasmin, Rasool Shah, Abdul Hamid Ganie, Khaled Moaddy

{"title":"Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation","authors":"M. Mossa Al-Sawalha, Humaira Yasmin, Rasool Shah, Abdul Hamid Ganie, Khaled Moaddy","doi":"10.3390/fractalfract7100753","DOIUrl":"https://doi.org/10.3390/fractalfract7100753","url":null,"abstract":"This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations clearly depict the categorization of these stochastic soliton solutions as kink waves or shock waves, offering a clear description of these soliton behaviors within the context of the SFKSE framework. The paper also illustrates the flexibility of the transformation-based approach mEDAM for investigating soliton occurrence not only in SFKSE but also in a wide range of nonlinear fractional partial differential equations (FPDEs). Furthermore, the analysis considers the effect of noise, specifically Brownian motion, on soliton solutions and wave dynamics, revealing the significant influence of randomness on the propagation, generation, and stability of soliton in complex stochastic systems and advancing our understanding of extreme behaviors in scientific and engineering domains.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014224","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: 3

Distributed Adaptive Optimization Algorithm for Fractional High-Order Multiagent Systems Based on Event-Triggered Strategy and Input Quantization 基于事件触发策略和输入量化的分数阶多智能体系统分布式自适应优化算法

2区数学

Fractal and Fractional Pub Date : 2023-10-11 DOI: 10.3390/fractalfract7100749

Xiaole Yang, Jiaxin Yuan, Tao Chen, Hui Yang

{"title":"Distributed Adaptive Optimization Algorithm for Fractional High-Order Multiagent Systems Based on Event-Triggered Strategy and Input Quantization","authors":"Xiaole Yang, Jiaxin Yuan, Tao Chen, Hui Yang","doi":"10.3390/fractalfract7100749","DOIUrl":"https://doi.org/10.3390/fractalfract7100749","url":null,"abstract":"This paper investigates the distributed optimization problem (DOP) for fractional high-order nonstrict-feedback multiagent systems (MASs) where each agent is multiple-input–multiple-output (MIMO) dynamic and contains uncertain dynamics. Based on the penalty-function method, the consensus constraint is eliminated and the global objective function is reconstructed. Different from the existing literatures, where the DOPs are addressed for linear MASs, this paper deals with the DOP through using radial basis function neural networks (RBFNNs) to approximate the unknown nonlinear functions for high-order MASs. To reduce transmitting and computational costs, event-triggered scheme and quantized control technology are combined to propose an adaptive backstepping neural network (NN) control protocol. By applying the Lyapunov stability theory, the optimal consensus error is proved to be bounded and all signals remain semi-global uniformly ultimately bounded. Simulation shows that all agents reach consensus and errors between agents’ outputs and the optimal solution is close to zero with low computational costs.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136213009","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

Approximation of Caputo Fractional Derivative and Numerical Solutions of Fractional Differential Equations 卡普托分数阶导数的近似与分数阶微分方程的数值解

2区数学

Fractal and Fractional Pub Date : 2023-10-11 DOI: 10.3390/fractalfract7100750

Yuri Dimitrov, Slavi Georgiev, Venelin Todorov

引用次数: 0

A Joint Multifractal Approach to Solar Wind Turbulence 太阳风湍流的联合多重分形方法

2区数学

Fractal and Fractional Pub Date : 2023-10-11 DOI: 10.3390/fractalfract7100748

Giuseppe Consolini, Paola De Michelis

引用次数: 0