Fractional Calculus and Applied Analysis最新文献

Unification of popular artificial neural network activation functions 统一流行的人工神经网络激活函数

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-30 DOI: 10.1007/s13540-024-00347-4

Mohammad Mostafanejad

引用次数: 0

Discrete-time general fractional calculus 离散时间一般分数微积分

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-21 DOI: 10.1007/s13540-024-00350-9

Alexandra V. Antoniouk, Anatoly N. Kochubei

引用次数: 0

The well-posedness analysis in Besov-type spaces for multi-term time-fractional wave equations 多期时间分式波方程在贝索夫类型空间中的拟合分析

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-21 DOI: 10.1007/s13540-024-00348-3

Yubin Liu, Li Peng

引用次数: 0

On the computation of the Mittag-Leffler function of fractional powers of accretive operators 关于分数幂增量算子的米塔格-勒弗勒函数的计算

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-21 DOI: 10.1007/s13540-024-00349-2

Eleonora Denich, Paolo Novati

引用次数: 0

A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids 一般非均匀网格上双面空间分数扩散方程的快速分数块中心有限差分法

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-18 DOI: 10.1007/s13540-024-00346-5

Meijie Kong, Hongfei Fu

{"title":"A fast fractional block-centered finite difference method for two-sided space-fractional diffusion equations on general nonuniform grids","authors":"Meijie Kong, Hongfei Fu","doi":"10.1007/s13540-024-00346-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00346-5","url":null,"abstract":"In this paper, a two-sided variable-coefficient space-fractional diffusion equation with fractional Neumann boundary condition is considered. To conquer the weak singularity caused by nonlocal space-fractional differential operators, a fractional block-centered finite difference (BCFD) method on general nonuniform grids is proposed. However, this discretization still results in an unstructured dense coefficient matrix with huge memory requirement and computational complexity. To address this issue, a fast version fractional BCFD algorithm by employing the well-known sum-of-exponentials (SOE) approximation technique is also proposed. Based upon the Krylov subspace iterative methods, fast matrix-vector multiplications of the resulting coefficient matrices with any vector are developed, in which they can be implemented in only ({mathcal {O}}(MN_{exp})) operations per iteration without losing any accuracy compared to the direct solvers, where (N_{exp}ll M) is the number of exponentials in the SOE approximation. Moreover, the coefficient matrices do not necessarily need to be generated explicitly, while they can be stored in ({mathcal {O}}(MN_{exp})) memory by only storing some coefficient vectors. Numerical experiments are provided to demonstrate the efficiency and accuracy of the method.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142449546","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 Wiener chaos: Part 1 分数维纳混沌第 1 部分

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-08 DOI: 10.1007/s13540-024-00343-8

Elena Boguslavskaya, Elina Shishkina

{"title":"Fractional Wiener chaos: Part 1","authors":"Elena Boguslavskaya, Elina Shishkina","doi":"10.1007/s13540-024-00343-8","DOIUrl":"https://doi.org/10.1007/s13540-024-00343-8","url":null,"abstract":"In this paper, we introduce a fractional analogue of the Wiener polynomial chaos expansion. It is important to highlight that the fractional order relates to the order of chaos decomposition elements, and not to the process itself, which remains the standard Wiener process. The central instrument in our fractional analogue of the Wiener chaos expansion is the function denoted as ({mathcal {H}}_alpha (x,y)), referred to herein as a power-normalised parabolic cylinder function. Through careful analysis of several fundamental deterministic and stochastic properties, we affirm that this function essentially serves as a fractional extension of the Hermite polynomial. In particular, the power-normalised parabolic cylinder function with the Wiener process and time as its arguments, ({mathcal {H}}_alpha (W_t,t)), demonstrates martingale properties and can be interpreted as a fractional Itô integral with 1 as the integrand, thereby drawing parallels with its non-fractional counterpart. To build a fractional analogue of polynomial Wiener chaos on the real line, we introduce a new function, which we call the extended Hermite function, by smoothly joining two power-normalized parabolic cylinder functions at zero. We form an orthogonal set of extended Hermite functions as a one-parameter family and use tensor products of the extended Hermite functions as building blocks in the fractional Wiener chaos expansion, in the same way that tensor products of Hermite polynomials are used as building blocks in the Wiener chaos polynomial expansion.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142385848","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

Variable-order fractional 1-Laplacian diffusion equations for multiplicative noise removal 用于消除乘法噪声的变阶分数 1-Laplacian 扩散方程

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-08 DOI: 10.1007/s13540-024-00345-6

Yuhang Li, Zhichang Guo, Jingfeng Shao, Yao Li, Boying Wu

引用次数: 0

A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems 用于计算能源系统中功率流问题解决方案的分数阶派生牛顿-拉斐森方法

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-08 DOI: 10.1007/s13540-024-00342-9

Francisco Damasceno Freitas, Laice Neves de Oliveira

{"title":"A Fractional Order Derivative Newton-Raphson Method for the Computation of the Power Flow Problem Solution in Energy Systems","authors":"Francisco Damasceno Freitas, Laice Neves de Oliveira","doi":"10.1007/s13540-024-00342-9","DOIUrl":"https://doi.org/10.1007/s13540-024-00342-9","url":null,"abstract":"Some nonlinear real-valued equations have no solution in the real number field, and only roots of this nature are of practical interest. However, complex roots associated with the solution may introduce an interpretation of the physical problem analysis. This paper investigates the solution of nonlinear equations exploiting fractional order derivative (FOD) calculus resources. The theory addresses a solver that considers the FOD and Newton-Raphson method. The problem is extended to a multivariate fractional order derivative (MFOD) method so that a set of nonlinear equations can be resolved iteratively. Applications to the computation of the power flow problem in energy systems are used to illustrate some types of equations and solutions. The MFOD uses a numerical limits technique to determine a Jacobian required for the fractional application. This work demonstrates how real-valued nonlinear equations with complex roots can be solved by the MFOD Newton-Raphson approach. The results indicate the potentiality of the method reaches complex-valued solutions despite the iterative process starting with a real-valued guess. The complex-valued results are interpreted considering the connection between the imaginary part of a root and the divergence of the classical Newton-Raphson (CNR) method.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142385763","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 Sobolev type spaces of functions of two variables via Riemann-Liouville derivatives 通过黎曼-刘维尔导数计算两变量函数的分数索波列夫类型空间

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-10-07 DOI: 10.1007/s13540-024-00344-7

Dariusz Idczak

引用次数: 0

Sticky Brownian motions on star graphs 星图上的粘性布朗运动

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-09-18 DOI: 10.1007/s13540-024-00336-7

Stefano Bonaccorsi, Mirko D’Ovidio

引用次数: 0