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Non-confluence of fractional stochastic differential equations driven by Lévy process 由列维过程驱动的分数随机微分方程的非融合性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-03 DOI: 10.1007/s13540-024-00278-0
Zhi Li, Tianquan Feng, Liping Xu
{"title":"Non-confluence of fractional stochastic differential equations driven by Lévy process","authors":"Zhi Li, Tianquan Feng, Liping Xu","doi":"10.1007/s13540-024-00278-0","DOIUrl":"https://doi.org/10.1007/s13540-024-00278-0","url":null,"abstract":"<p>In this paper, we investigate a class of stochastic Riemann-Liouville type fractional differential equations driven by Lévy noise. By using Itô formula for the considered equation, we attempt to explore the non-confluence property of solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions which is novel in exploring the non-confluence property of differential equations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"88 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140895909","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
Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem 对数拉普拉奇问题的霍普夫定理和径向对称性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-03 DOI: 10.1007/s13540-024-00285-1
Lihong Zhang, Xiaofeng Nie
{"title":"Hopf’s lemma and radial symmetry for the Logarithmic Laplacian problem","authors":"Lihong Zhang, Xiaofeng Nie","doi":"10.1007/s13540-024-00285-1","DOIUrl":"https://doi.org/10.1007/s13540-024-00285-1","url":null,"abstract":"<p>In this paper, we prove Hopf’s lemma for the Logarithmic Laplacian. At first, we introduce the strong minimum principle. Then Hopf’s lemma for the Logarithmic Laplacian in the ball is proved. On this basis, Hopf’s lemma of the Logarithmic Laplacian is extended to any open set with the property of the interior ball. Finally, an example is given to explain Hopf’s lemma can be applied to the study of the symmetry of the positive solution of the nonlinear Logarithmic Laplacian problem by the moving plane method.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"56 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140895809","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
Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation 多期时间分数波方程系数反问题的隶属原理应用
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-29 DOI: 10.1007/s13540-024-00284-2
Emilia Bazhlekova
{"title":"Application of subordination principle to coefficient inverse problem for multi-term time-fractional wave equation","authors":"Emilia Bazhlekova","doi":"10.1007/s13540-024-00284-2","DOIUrl":"https://doi.org/10.1007/s13540-024-00284-2","url":null,"abstract":"<p>An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, <span>(alpha )</span> and <span>(alpha _m)</span>, it is assumed <span>(1&lt;alpha &lt;2)</span> and <span>(alpha -alpha _mle 1)</span>. Subordination principle with respect to the corresponding single-term time-fractional wave equation of order <span>(alpha )</span> is deduced. Injectivity of the integral transform, defined by the subordination relation, is established. The subordination identity is used to prove uniqueness for a coefficient inverse problem for the multi-term equation, based on an analogous property for the related single-term one. In addition, the subordination relation is applied for deriving a regularity estimate.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"24 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140814826","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
Monotone iterative technique for multi-term time fractional measure differential equations 多期时间分数计量微分方程的单调迭代技术
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-17 DOI: 10.1007/s13540-024-00273-5
Haide Gou, Min Shi
{"title":"Monotone iterative technique for multi-term time fractional measure differential equations","authors":"Haide Gou, Min Shi","doi":"10.1007/s13540-024-00273-5","DOIUrl":"https://doi.org/10.1007/s13540-024-00273-5","url":null,"abstract":"<p>In this paper, we investigate the existence and uniqueness of the <i>S</i>-asymptotically <span>(omega )</span>-periodic mild solutions to a class of multi-term time-fractional measure differential equations with nonlocal conditions in an ordered Banach spaces. Firstly, we look for suitable concept of <i>S</i>-asymptotically <span>(omega )</span>-periodic mild solution to our concern problem, by means of Laplace transform and <span>((beta ,gamma _k))</span>-resolvent family <span>({S_{beta ,gamma _k}(t)}_{tge 0})</span>. Secondly, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed fractional measure differential equations, and obtain the existence of maximal and minimal <i>S</i>-asymptotically <span>(omega )</span>-periodic mild solutions for the mentioned system. Finally, as the application of abstract results, an example is given to illustrate our main results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"50 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140620453","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":"2012 1","pages":""},"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":"1 1","pages":""},"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":"129 1","pages":""},"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":"38 1","pages":""},"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":"158 1","pages":""},"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":"33 1","pages":""},"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
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