Fractional Calculus and Applied Analysis最新文献_第9页

Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory 针对热传导中出现的非局部演化方程的θ型卷积正交 OSC 记忆法

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-25 DOI: 10.1007/s13540-024-00265-5

Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy

{"title":"Theta-type convolution quadrature OSC method for nonlocal evolution equations arising in heat conduction with memory","authors":"Leijie Qiao, Wenlin Qiu, M. A. Zaky, A. S. Hendy","doi":"10.1007/s13540-024-00265-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00265-5","url":null,"abstract":"In this paper, we propose a robust and simple technique with efficient algorithmic implementation for numerically solving the nonlocal evolution problems. A theta-type ((theta )-type) convolution quadrature rule is derived to approximate the nonlocal integral term in the problem under consideration, such that (theta in (frac{1}{2},1)), which remains untreated in the literature. The proposed approaches are based on the (theta ) method ((frac{1}{2}le theta le 1)) for the time derivative and the constructed (theta )-type convolution quadrature rule for the fractional integral term. A detailed error analysis of the proposed scheme is provided with respect to the usual convolution kernel and the tempered one. In order to fully discretize our problem, we implement the orthogonal spline collocation (OSC) method with piecewise Hermite bicubic for spatial operators. Stability and error estimates of the proposed (theta )-OSC schemes are discussed. Finally, some numerical experiments are introduced to demonstrate the efficiency of our theoretical findings.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140209884","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

Relative controllability of linear state-delay fractional systems 线性状态延迟分数系统的相对可控性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-25 DOI: 10.1007/s13540-024-00270-8

引用次数: 0

Diffusion equations with spatially dependent coefficients and fractal Cauer-type networks 具有空间依赖系数的扩散方程和分形考尔型网络

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-22 DOI: 10.1007/s13540-024-00264-6

引用次数: 0

Asymptotical stabilization of fuzzy semilinear dynamic systems involving the generalized Caputo fractional derivative for $$q in (1,2)$$ 涉及 $$q in (1,2)$$ 的广义卡普托分数导数的模糊半线性动态系统的渐近稳定问题

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-20 DOI: 10.1007/s13540-024-00268-2

Truong Vinh An, Vasile Lupulescu, Ngo Van Hoa

引用次数: 0

Rich phenomenology of the solutions in a fractional Duffing equation 分数达芬方程中丰富的解现象学

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-20 DOI: 10.1007/s13540-024-00269-1

Sara Hamaizia, Salvador Jiménez, M. Pilar Velasco

引用次数: 0

Sum of series and new relations for Mittag-Leffler functions Mittag-Leffler 函数的级数之和与新关系式

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-19 DOI: 10.1007/s13540-024-00266-4

Sarah A. Deif, E. Capelas de Oliveira

引用次数: 0

Global optimization of a nonlinear system of differential equations involving $$psi $$ -Hilfer fractional derivatives of complex order 涉及复阶 $$psi $$ -Hilfer 分数导数的非线性微分方程系统的全局优化

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-11 DOI: 10.1007/s13540-024-00260-w

引用次数: 0

Asymptotic analysis of three-parameter Mittag-Leffler function with large parameters, and application to sub-diffusion equation involving Bessel operator 具有大参数的三参数 Mittag-Leffler 函数的渐近分析，以及在涉及贝塞尔算子的子扩散方程中的应用

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-11 DOI: 10.1007/s13540-024-00263-7

Hassan Askari, Alireza Ansari

引用次数: 0

Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter 有参数极值的分数基尔霍夫问题的内哈里流形方法

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-05 DOI: 10.1007/s13540-024-00261-9

{"title":"Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter","authors":"","doi":"10.1007/s13540-024-00261-9","DOIUrl":"https://doi.org/10.1007/s13540-024-00261-9","url":null,"abstract":"<h3>Abstract</h3> In this work we study the following nonlocal problem $$begin{aligned} left{ begin{aligned} M(Vert uVert ^2_X)(-varDelta )^s u&= lambda {f(x)}|u|^{gamma -2}u+{g(x)}|u|^{p-2}u{} & {} text{ in } varOmega , u&=0{} & {} text{ on } mathbb R^Nsetminus varOmega , end{aligned} right. end{aligned}$$ where (varOmega subset mathbb R^N) is open and bounded with smooth boundary, (N>2s, sin (0, 1), M(t)=a+bt^{theta -1},;tge 0) with ( theta >1, age 0) and (b>0) . The exponents satisfy (1<gamma<2<{2theta<p<2^*_{s}=2N/(N-2s)}) (when (ane 0) ) and (2<gamma<2theta<p<2^*_{s}) (when (a=0) ). The parameter (lambda ) involved in the problem is real and positive. The problem under consideration has nonlocal behaviour due to the presence of nonlocal fractional Laplacian operator as well as the nonlocal Kirchhoff term (M(Vert uVert ^2_X)) , where (Vert uVert ^{2}_{X}=iint _{mathbb R^{2N}} frac{|u(x)-u(y)|^2}{left| x-yright| ^{N+2s}}dxdy) . The weight functions (f, g:varOmega rightarrow mathbb R) are continuous, f is positive while g is allowed to change sign. In this paper an extremal value of the parameter, a threshold to apply Nehari manifold method, is characterized variationally for both degenerate and non-degenerate Kirchhoff cases to show an existence of at least two positive solutions even when (lambda ) crosses the extremal parameter value by executing fine analysis based on fibering maps and Nehari manifold.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032365","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

Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices 稀疏 SPD 矩阵分数幂的 BURA 和基于 BURA 的近似分析

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2024-03-04 DOI: 10.1007/s13540-024-00256-6

Nikola Kosturski, Svetozar Margenov

{"title":"Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices","authors":"Nikola Kosturski, Svetozar Margenov","doi":"10.1007/s13540-024-00256-6","DOIUrl":"https://doi.org/10.1007/s13540-024-00256-6","url":null,"abstract":"Numerical methods applicable to the approximation of spectral fractional diffusion operators in multidimensional domains with general geometry are analyzed. Over the past decade, several approaches have been proposed to approximate the inverse operator (mathcal {A}^{-alpha }), (alpha in (0,1)). Despite their different origins, they can all be written as a rational approximation. Let the matrix (mathbb {A}) be obtained after finite difference or finite element discretization of (mathcal {A}). The BURA (Best Uniform Rational Approximation) method was introduced to approximate the inverse matrix ({mathbb A}^{-alpha }) based on an approximation of the scallar function (z^alpha ), (alpha in (0,1)), (zin [0,1]). In this paper we study BURA and BURA-based methods for fractional powers of sparse symmetric and positive definite (SPD) matrices, presentiing the concept, general framework and error analysis. Our contributions concern approximations of (mathbb {A}^{-alpha }) and (mathbb {A}^alpha ) for arbitrary (alpha > 0), thus significantly expanding the range of available currently results. Assymptotically accurate error estimates are obtained. The rate of convergence is exponential with respect to the degree of BURA. Numerical results are presented to illustrate and better interpret the theoretical estimates.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032319","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