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Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise 更正：带有综合乘法噪声的半线性随机子扩散的存在性、唯一性和正则性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-12 DOI: 10.1007/s13540-024-00280-6
Zhiqiang Li, Yubin Yan
{"title":"Correction: Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise","authors":"Zhiqiang Li, Yubin Yan","doi":"10.1007/s13540-024-00280-6","DOIUrl":"https://doi.org/10.1007/s13540-024-00280-6","url":null,"abstract":"","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140708734","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
A tempered subdiffusive Black–Scholes model 一个有节制的亚扩散布莱克-斯科尔斯模型
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-09 DOI: 10.1007/s13540-024-00276-2
Grzegorz Krzyżanowski, Marcin Magdziarz
{"title":"A tempered subdiffusive Black–Scholes model","authors":"Grzegorz Krzyżanowski, Marcin Magdziarz","doi":"10.1007/s13540-024-00276-2","DOIUrl":"https://doi.org/10.1007/s13540-024-00276-2","url":null,"abstract":"<p>In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order <span>(2-alpha )</span> with respect to time, where <span>(alpha in (0,1))</span> is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140541419","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
Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians 涉及不同分数拉普拉斯的耦合 k-Hessian 系统的非负解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-09 DOI: 10.1007/s13540-024-00277-1
Lihong Zhang, Qi Liu, Bashir Ahmad, Guotao Wang
{"title":"Nonnegative solutions of a coupled k-Hessian system involving different fractional Laplacians","authors":"Lihong Zhang, Qi Liu, Bashir Ahmad, Guotao Wang","doi":"10.1007/s13540-024-00277-1","DOIUrl":"https://doi.org/10.1007/s13540-024-00277-1","url":null,"abstract":"<p>This paper studies the following coupled <i>k</i>-Hessian system with different order fractional Laplacian operators: </p><span>$$begin{aligned} {left{ begin{array}{ll} {S_k}({D^2}w(x))-A(x)(-varDelta )^{alpha /2}w(x)=f(z(x)), {S_k}({D^2}z(x))-B(x)(-varDelta )^{beta /2}z(x)=g(w(x)). end{array}right. } end{aligned}$$</span><p>Firstly, we discuss <i>decay at infinity principle</i> and <i>narrow region principle</i> for the <i>k</i>-Hessian system involving fractional order Laplacian operators. Then, by exploiting the direct method of moving planes, the radial symmetry and monotonicity of the nonnegative solutions to the coupled <i>k</i>-Hessian system are proved in a unit ball and the whole space, respectively. We believe that the present work will lead to a deep understanding of the coupled <i>k</i>-Hessian system involving different order fractional Laplacian operators.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140541241","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
Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces 在 $$p$ -adic 混合中心莫雷空间和广义混合莫雷空间上的 $$p$ -adic 分数积分算子及其换元子的估计值
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-08 DOI: 10.1007/s13540-024-00274-4
Naqash Sarfraz, Muhammad Aslam, Qasim Ali Malik
{"title":"Estimates for $$p$$ -adic fractional integral operators and their commutators on $$p$$ -adic mixed central Morrey spaces and generalized mixed Morrey spaces","authors":"Naqash Sarfraz, Muhammad Aslam, Qasim Ali Malik","doi":"10.1007/s13540-024-00274-4","DOIUrl":"https://doi.org/10.1007/s13540-024-00274-4","url":null,"abstract":"<p>In this paper, we define the <span>(p)</span>-adic mixed Morrey type spaces and study the boundedness of <span>(p)</span>-adic fractional integral operators and their commutators on these spaces. More precisely, we first obtain the boundedness of <span>(p)</span>-adic fractional integral operators and their commutators on <span>(p)</span>-adic mixed central Morrey spaces. Moreover, we further extend these results on <span>(p)</span>-adic generalized mixed Morrey spaces, when a symbol function <span>(b)</span> belongs to the <span>(p)</span>-adic generalized mixed Campanato spaces.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140534227","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
Subordination results for a class of multi-term fractional Jeffreys-type equations 一类多项式分式杰弗里斯型方程的服从结果
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-04 DOI: 10.1007/s13540-024-00275-3
Emilia Bazhlekova
{"title":"Subordination results for a class of multi-term fractional Jeffreys-type equations","authors":"Emilia Bazhlekova","doi":"10.1007/s13540-024-00275-3","DOIUrl":"https://doi.org/10.1007/s13540-024-00275-3","url":null,"abstract":"<p>Jeffreys equation and its fractional generalizations provide extensions of the classical diffusive laws of Fourier and Fick for heat and particle transport. In this work, a class of multi-term time-fractional generalizations of the classical Jeffreys equation is studied. Restrictions on the parameters are derived, which ensure that the fundamental solution to the one-dimensional Cauchy problem is a spatial probability density function evolving in time. The studied equations are recast as Volterra integral equations with kernels represented in terms of multinomial Mittag-Leffler functions. Applying operator-theoretic approach, we establish subordination results with respect to appropriate evolution equations of integer order, depending on the considered range of parameters. Analyticity of the corresponding solution operator is also discussed. The main tools in the proofs are Laplace transform and the Bernstein functions’ technique, especially, some properties of the sets of real powers of complete Bernstein functions.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140349597","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
Collage theorems, invertibility and fractal functions 拼贴定理、可逆性和分形函数
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-03 DOI: 10.1007/s13540-024-00281-5
{"title":"Collage theorems, invertibility and fractal functions","authors":"","doi":"10.1007/s13540-024-00281-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00281-5","url":null,"abstract":"<h3>Abstract</h3> <p>Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140343566","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
Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations 三维时间分数布辛斯-科里奥利方程的全局存在性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-03-26 DOI: 10.1007/s13540-024-00272-6
Jinyi Sun, Chunlan Liu, Minghua Yang
{"title":"Global existence for three-dimensional time-fractional Boussinesq-Coriolis equations","authors":"Jinyi Sun, Chunlan Liu, Minghua Yang","doi":"10.1007/s13540-024-00272-6","DOIUrl":"https://doi.org/10.1007/s13540-024-00272-6","url":null,"abstract":"<p>The paper is concerned with the three-dimensional Boussinesq-Coriolis equations with Caputo time-fractional derivatives. Specifically, by striking new balances between the dispersion effects of the Coriolis force and the smoothing effects of the Laplacian dissipation involving with a time-fractional evolution mechanism, we obtain the global existence of mild solutions to Cauchy problem of three-dimensional time-fractional Boussinesq-Coriolis equations in Besov spaces.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303485","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
Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces 非紧凑性新量度在广义莫雷空间非线性和分数积分方程系统可解性中的应用
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-03-26 DOI: 10.1007/s13540-024-00262-8
Hengameh Tamimi, S. Saiedinezhad, M. Ghaemi
{"title":"Applications of a new measure of noncompactness to the solvability of systems of nonlinear and fractional integral equations in the generalized Morrey spaces","authors":"Hengameh Tamimi, S. Saiedinezhad, M. Ghaemi","doi":"10.1007/s13540-024-00262-8","DOIUrl":"https://doi.org/10.1007/s13540-024-00262-8","url":null,"abstract":"","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378215","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
Transformations of the matrices of the fractional linear systems to their canonical stable forms 将分数线性系统的矩阵变换为其典型稳定形式
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-03-26 DOI: 10.1007/s13540-024-00271-7
Tadeusz Kaczorek, Lukasz Sajewski
{"title":"Transformations of the matrices of the fractional linear systems to their canonical stable forms","authors":"Tadeusz Kaczorek, Lukasz Sajewski","doi":"10.1007/s13540-024-00271-7","DOIUrl":"https://doi.org/10.1007/s13540-024-00271-7","url":null,"abstract":"<p>A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the existence of the solution to the transformation problem of the linear system to its asymptotically stable controllable and observable canonical forms with desired eigenvalues are given and illustrated by numerical examples of fractional linear systems.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303568","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
Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus Mkhitar Djrbashian 对分数微积分的某些贡献
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-03-26 DOI: 10.1007/s13540-024-00267-3
{"title":"Some aspects of the contribution of Mkhitar Djrbashian to fractional calculus","authors":"","doi":"10.1007/s13540-024-00267-3","DOIUrl":"https://doi.org/10.1007/s13540-024-00267-3","url":null,"abstract":"<h3>Abstract</h3> <p>This survey shows the way in which the Armenian mathematician Academician M.M. Djrbashian introduced the apparatus of fractional calculus in investigation of weighted classes and spaces of regular functions since his earliest work of 1945 (see [<span>3</span>, <span>4</span>] or Addendum to [<span>22</span>]). The investigations of M.M. Djrbashian in this topic reached their final point by his exhaustive factorization theory for functions meromorphic in the unit disc of the complex plane [<span>11</span>]. The contemporary development of M.M. Djrbashian’s ideas can be found in the recent monograph [<span>22</span>]. The survey intends to complete the survey article “Mkhitar Djrbashian and his contribution to fractional calculus&quot; [<span>25</span>], which described the contribution of M.M. Djrbashian mainly from the point of view of basic constructions of the fractional calculus, to the theory of fractional differential equations and integral transforms.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140303155","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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