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Fractional Calculus and Applied Analysis最新文献

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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
{"title":"Sticky Brownian motions on star graphs","authors":"Stefano Bonaccorsi, Mirko D’Ovidio","doi":"10.1007/s13540-024-00336-7","DOIUrl":"https://doi.org/10.1007/s13540-024-00336-7","url":null,"abstract":"<p>This paper is concerned with the construction of Brownian motions and related stochastic processes in a star graph, which is a non-Euclidean structure where some features of the classical modeling fail. We propose a probabilistic construction of the Sticky Brownian motion by slowing down the Brownian motion when in the vertex of the star graph. Later, we apply a random change of time to the previous construction, which leads to a trapping phenomenon in the vertex of the star graph, with characterization of the trap in terms of a singular measure <span>(varPhi )</span>. The process associated to this time change is described here and, moreover, we show that it defines a probabilistic representation of the solution to a heat equation type problem on the star graph with non-local dynamic conditions in the vertex that can be written in terms of a Caputo-Džrbašjan fractional derivative defined by the singular measure <span>(varPhi )</span>. Extensions to general graph structures can be given by applying to our results a localisation technique.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142245217","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
Group classification of time fractional Black-Scholes equation with time-dependent coefficients 具有时间相关系数的时间分数 Black-Scholes 方程的分组分类
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-16 DOI: 10.1007/s13540-024-00339-4
Jicheng Yu, Yuqiang Feng
{"title":"Group classification of time fractional Black-Scholes equation with time-dependent coefficients","authors":"Jicheng Yu, Yuqiang Feng","doi":"10.1007/s13540-024-00339-4","DOIUrl":"https://doi.org/10.1007/s13540-024-00339-4","url":null,"abstract":"<p>In this paper, we present Lie symmetry analysis for time fractional Black-Scholes equation with time-dependent coefficients. The group classification is carried out by investigating the time-dependent coefficients <span>(sigma (t))</span>, <i>r</i>(<i>t</i>) and <i>s</i>(<i>t</i>). Then the obtained group generators are used to reduce the equation under study, some of the reduced equations are fractional ordinary equations with Erdélyi-Kober fractional derivative, and some exact solutions including power series solutions are constructed.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235035","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
Reconstruction of a fractional evolution equation with a source 重构带源的分数演化方程
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-16 DOI: 10.1007/s13540-024-00337-6
Amin Boumenir, Khaled M. Furati, Ibrahim O. Sarumi
{"title":"Reconstruction of a fractional evolution equation with a source","authors":"Amin Boumenir, Khaled M. Furati, Ibrahim O. Sarumi","doi":"10.1007/s13540-024-00337-6","DOIUrl":"https://doi.org/10.1007/s13540-024-00337-6","url":null,"abstract":"<p>We are concerned with the inverse problem of reconstructing a fractional evolution equation with a source. To this end we use observations of the solution on the boundary to reconstruct the principal part of the operator and the fractional order of the time derivative, while an overdetermination at a time <i>T</i> is used to recover the source by a non iterative method. Numerical examples explain how to compute the fractional order and the source using finite data.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235038","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
Optimal solvability for the fractional p-Laplacian with Dirichlet conditions 具有迪里夏特条件的分数 p-拉普拉奇的最优可解性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-13 DOI: 10.1007/s13540-024-00341-w
Antonio Iannizzotto, Dimitri Mugnai
{"title":"Optimal solvability for the fractional p-Laplacian with Dirichlet conditions","authors":"Antonio Iannizzotto, Dimitri Mugnai","doi":"10.1007/s13540-024-00341-w","DOIUrl":"https://doi.org/10.1007/s13540-024-00341-w","url":null,"abstract":"<p>We study a nonlinear, nonlocal Dirichlet problem driven by the fractional <i>p</i>-Laplacian, involving a <span>((p-1))</span>-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142175014","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
Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation 非自治分式 HLS 下临界 Choquard 方程归一化解的存在性、多重性和渐近行为
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-13 DOI: 10.1007/s13540-024-00338-5
Jianlun Liu, Hong-Rui Sun, Ziheng Zhang
{"title":"Existence, multiplicity and asymptotic behaviour of normalized solutions to non-autonomous fractional HLS lower critical Choquard equation","authors":"Jianlun Liu, Hong-Rui Sun, Ziheng Zhang","doi":"10.1007/s13540-024-00338-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00338-5","url":null,"abstract":"<p>In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function <i>h</i>, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of <i>h</i> when <span>(varepsilon )</span> is small enough.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142231538","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
Radial symmetry of positive solutions for a tempered fractional p-Laplacian system 节制分数 p-拉普拉斯系统正解的径向对称性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-12 DOI: 10.1007/s13540-024-00340-x
Xueying Chen
{"title":"Radial symmetry of positive solutions for a tempered fractional p-Laplacian system","authors":"Xueying Chen","doi":"10.1007/s13540-024-00340-x","DOIUrl":"https://doi.org/10.1007/s13540-024-00340-x","url":null,"abstract":"<p>In this paper, we consider the following Schrödinger system involving the tempered fractional <i>p</i>-Laplacian </p><span>$$begin{aligned} {left{ begin{array}{ll} begin{aligned} &amp; (-varDelta -lambda )^s_p u(x)+au^{p-1}(x)=f(u(x),v(x)), &amp; (-varDelta -lambda )^t_p v(x)+bv^{p-1}(x)=g(u(x),v(x)), end{aligned} end{array}right. } end{aligned}$$</span><p>where <span>(n ge 2)</span>, <span>(a, b&gt;0)</span>, <span>(2&lt;p&lt;infty )</span>, <span>(0&lt;s, t&lt;1)</span> and <span>(lambda )</span> is a sufficiently small positive constant. To effectively utilize the direct method of moving planes, we first establish the narrow region principle and the decay at infinity. Then we prove the radial symmetry and monotonicity of positive solutions for the system in the unit ball and the whole space. Our results are an extension of some content in Ma and Zhang (Appl Math J Chin Univ 37: 52–72, 2022).</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142175013","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
Overview of fractional calculus and its computer implementation in Wolfram Mathematica 分数微积分及其在 Wolfram Mathematica 中的计算机实现概述
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-11 DOI: 10.1007/s13540-024-00332-x
Oleg Marichev, Elina Shishkina
{"title":"Overview of fractional calculus and its computer implementation in Wolfram Mathematica","authors":"Oleg Marichev, Elina Shishkina","doi":"10.1007/s13540-024-00332-x","DOIUrl":"https://doi.org/10.1007/s13540-024-00332-x","url":null,"abstract":"<p>This survey aims to present various approaches to non-integer integrals and derivatives and their practical implementation within Wolfram Mathematica. It begins by short discussion of historical moments and applications related to fractional calculus. Different methods for handling non-integer powers of differentiation operators are presented, along with generalizations of fractional integrals and derivatives. The survey also delves into the diverse applications of fractional calculus in physics, engineering, medicine, and numerical calculations. Essential details of fractional integro-differentiation implemented in Wolfram Mathematica are highlighted. The Hadamard regularization of Riemann-Liouville operator is utilized as the foundation for creating the arbitrary order of integro-differential operator in Mathematica. The survey describes the application of fractional integro-differentiation to Taylor series expansions near zero using Hadamard regularization and the use of the Meijer <i>G</i>-function for evaluating derivatives of complex orders. We conclude with a discussion on applying fractional integro-differentiation to “differential constants” and provide generic formulas for fractional differentiation. The extensive list of references underscores the vast body of works on fractional calculus.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142170844","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
Non-confluence for SDEs driven by fractional Brownian motion with Markovian switching 具有马尔可夫切换的分数布朗运动驱动的 SDE 的非汇合问题
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-09 DOI: 10.1007/s13540-024-00334-9
Zhi Li, Benchen Huang, Liping Xu
{"title":"Non-confluence for SDEs driven by fractional Brownian motion with Markovian switching","authors":"Zhi Li, Benchen Huang, Liping Xu","doi":"10.1007/s13540-024-00334-9","DOIUrl":"https://doi.org/10.1007/s13540-024-00334-9","url":null,"abstract":"<p>In this paper, we investigate the non-confluence property of a class of stochastic differential equations with Markovian switching driven by fractional Brownian motion with Hurst parameter <span>(Hin (1/2,1))</span>. By using the generalized Itô formula and stopping time techniques, we obtain some sufficient conditions ensuring the non-confluence property for the considered equations. Additionally, we present two important corollaries on the non-confluence property by the Poisson equation and <i>M</i>-matrix, respectively, which can verify the non-confluence property more effectively than the general condition. Finally, we provide an example to illustrate the practical usefulness of our theoretical results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142160425","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
Stepanov-like weighted pseudo S-asymptotically Bloch type periodicity and applications to stochastic evolution equations with fractional Brownian motions 斯捷潘诺夫类加权伪 S-渐近布洛赫型周期性及其在分数布朗运动随机演化方程中的应用
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-06 DOI: 10.1007/s13540-024-00333-w
Amadou Diop, Mamadou Moustapha Mbaye, Yong-Kui Chang, Gaston Mandata N’Guérékata
{"title":"Stepanov-like weighted pseudo S-asymptotically Bloch type periodicity and applications to stochastic evolution equations with fractional Brownian motions","authors":"Amadou Diop, Mamadou Moustapha Mbaye, Yong-Kui Chang, Gaston Mandata N’Guérékata","doi":"10.1007/s13540-024-00333-w","DOIUrl":"https://doi.org/10.1007/s13540-024-00333-w","url":null,"abstract":"<p>In this paper, we introduce the concept of Stepanov-like (weighted) pseudo <i>S</i>-asymptotically Bloch type periodic processes in the square mean sense, and establish some basic results on the function space of such processes like completeness, convolution and composition theorems. Under the situation that the functions forcing are Stepanov-like (weighted) pseudo <i>S</i>-asymptotically Bloch type periodic and verify some suitable assumptions, we establish the existence and uniqueness of square-mean (weighted) pseudo <i>S</i>-asymptotically Bloch type periodic mild solutions of some fractional stochastic integrodifferential equations (driven by fractional Brownian motion). Finally, the most important findings are substantiated with the assistance of an illustration.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144251","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
An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise 具有随机系数和分数积分乘法噪声的随机分数热方程的高效数值方法
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-09-06 DOI: 10.1007/s13540-024-00335-8
Xiao Qi, Chuanju Xu
{"title":"An efficient numerical method to the stochastic fractional heat equation with random coefficients and fractionally integrated multiplicative noise","authors":"Xiao Qi, Chuanju Xu","doi":"10.1007/s13540-024-00335-8","DOIUrl":"https://doi.org/10.1007/s13540-024-00335-8","url":null,"abstract":"<p>This paper studies the stochastic time-fractional heat diffusion equation involving a Caputo derivative in time of order <span>(alpha in (frac{1}{2},1])</span>, driven simultaneously by a random diffusion coefficient field and fractionally integrated multiplicative noise. First, the well-posedness of the underlying problem is established by proving the existence, uniqueness, and stability of the mild solution. Then a spatio-temporal discretization method based on a Milstein exponential integrator scheme and finite element method is constructed and analyzed. The strong convergence rate of the fully discrete solution is derived. Numerical experiments are finally reported to confirm the theoretical result.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142144300","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
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