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S-asymptotically $$omega $$ -periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms 具有超线性增长非线性项的时空分数非局部反应扩散方程的 S-渐近 $$omega $$ - 周期解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-14 DOI: 10.1007/s13540-024-00325-w
Pengyu Chen, Kaibo Ding, Xuping Zhang
{"title":"S-asymptotically $$omega $$ -periodic solutions for time-space fractional nonlocal reaction-diffusion equation with superlinear growth nonlinear terms","authors":"Pengyu Chen, Kaibo Ding, Xuping Zhang","doi":"10.1007/s13540-024-00325-w","DOIUrl":"https://doi.org/10.1007/s13540-024-00325-w","url":null,"abstract":"<p>This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related <i>S</i>-asymptotically <span>(omega )</span>-periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can grow any number of orders, we discuss the existence and uniqueness of <i>S</i>-asymptotically <span>(omega )</span>-periodic solutions based on the theory of operator semigroups and fixed point theorem. In addition, we considered the Mittag-Leffler-Ulam-Hyers stability results using the singular type Gronwall inequality and appropriate fractional calculus. The results in the present paper extended the work of (Andrade et al. in Proc Edinb Math Soc 59:65–76, 2016) to the case of time-space fractional nonlocal reaction-diffusion equations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"80 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141986585","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
Computing the Mittag-Leffler function of a matrix argument 计算矩阵参数的 Mittag-Leffler 函数
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-13 DOI: 10.1007/s13540-024-00326-9
João R. Cardoso
{"title":"Computing the Mittag-Leffler function of a matrix argument","authors":"João R. Cardoso","doi":"10.1007/s13540-024-00326-9","DOIUrl":"https://doi.org/10.1007/s13540-024-00326-9","url":null,"abstract":"<p>It is well-known that the two-parameter Mittag-Leffler (ML) function plays a key role in Fractional Calculus. In this paper, we address the problem of computing this function, when its argument is a square matrix. Effective methods for solving this problem involve the computation of higher order derivatives or require the use of mixed precision arithmetic. In this paper, we provide an alternative method that is derivative-free and works entirely using IEEE standard double precision arithmetic. If certain conditions are satisfied, our method uses a Taylor series representation for the ML function; if not, it switches to a Schur-Parlett technique that will be combined with the Cauchy integral formula. A detailed discussion on the choice of a convenient contour is included. Theoretical and numerical issues regarding the performance of the proposed algorithm are discussed. A set of numerical experiments shows that our novel approach is competitive with the state-of-the-art method for IEEE double precision arithmetic, in terms of accuracy and CPU time. For matrices whose Schur decomposition has large blocks with clustered eigenvalues, our method far outperforms the other. Since our method does not require the efficient computation of higher order derivatives, it has the additional advantage of being easily extended to other matrix functions (e.g., special functions).</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"94 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141980925","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 differential equation on the whole axis involving Liouville derivative 涉及刘维尔导数的整轴微分方程
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-12 DOI: 10.1007/s13540-024-00327-8
Ivan Matychyn, Viktoriia Onyshchenko
{"title":"Fractional differential equation on the whole axis involving Liouville derivative","authors":"Ivan Matychyn, Viktoriia Onyshchenko","doi":"10.1007/s13540-024-00327-8","DOIUrl":"https://doi.org/10.1007/s13540-024-00327-8","url":null,"abstract":"<p>The paper investigates fractional differential equations involving the Liouville derivative. Solution to these equations under a boundary condition inside the time interval are derived in explicit form, their uniqueness is established using integral transforms technique.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"16 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141974006","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
On some fractional parabolic reaction-diffusion systems with gradient source terms 关于一些带有梯度源项的分数抛物线反应扩散系统
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-12 DOI: 10.1007/s13540-024-00316-x
Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri
{"title":"On some fractional parabolic reaction-diffusion systems with gradient source terms","authors":"Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri","doi":"10.1007/s13540-024-00316-x","DOIUrl":"https://doi.org/10.1007/s13540-024-00316-x","url":null,"abstract":"<p>The present paper is concerned with a fractional parabolic reaction-diffusion system posed in a regular bounded open subset of <span>({mathbb {R}}^N)</span>, where the gradients of the unknowns act as source terms (see (<i>S</i>) below). First, we establish some nonexistence and blow-up in finite time results. Second, we prove some new weighted regularity results. Such results are interesting in themselves and play a crucial role to study local existence of nonnegative solutions to our system under suitable assumptions on the data. This work also highlights a substantial difference between the nonlocal case and the local case already studied by the fourth author and his coworkers.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"4 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141974005","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
Quasi Limiting Distributions on generalized non-local in time and discrete-state stochastic processes 广义非局部时间和离散状态随机过程的准极限分布
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-12 DOI: 10.1007/s13540-024-00312-1
Jorge Littin Curinao
{"title":"Quasi Limiting Distributions on generalized non-local in time and discrete-state stochastic processes","authors":"Jorge Littin Curinao","doi":"10.1007/s13540-024-00312-1","DOIUrl":"https://doi.org/10.1007/s13540-024-00312-1","url":null,"abstract":"<p>In this article, we study the asymptotic behavior of a discrete space-state and continuous-time killed process <span>(({widetilde{X}}^{nu }(t))_{t ge 0})</span> whose transition probabilities are governed by a non-local convolution type-operator <span>(mathcal {D}^{nu })</span>. Approximation formulas are provided for small and large values of <span>(t ge 0)</span>. In the latter case, the problem of the existence of a Quasi limiting distribution (QLD) is studied in detail, proving that (i) The QLD strongly depends on the initial distribution and (ii) the definition of Quasi Stationary Distribution (QSD) and QLD differs, excepting some very particular cases. Previous to the statement of our main results, a detailed description of our kind of processes is presented. This article generalizes the previous work [25], which is focused on a one-dimensional fractional birth and death process with transition probabilities governed by a fractional Caputo-Dzhrbashyan derivative.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"375 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141974004","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 and Liouville theorem for master equations 主方程的径向对称性和柳维尔定理
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-12 DOI: 10.1007/s13540-024-00328-7
Lingwei Ma, Yahong Guo, Zhenqiu Zhang
{"title":"Radial symmetry and Liouville theorem for master equations","authors":"Lingwei Ma, Yahong Guo, Zhenqiu Zhang","doi":"10.1007/s13540-024-00328-7","DOIUrl":"https://doi.org/10.1007/s13540-024-00328-7","url":null,"abstract":"<p>This paper has two primary objectives. The first one is to demonstrate that the solutions of master equation </p><span>$$begin{aligned} (partial _t-Delta )^s u(x,t) =f(u(x, t)), ,,(x, t)in B_1(0)times mathbb {R}, end{aligned}$$</span><p>subject to the vanishing exterior condition, are radially symmetric and strictly decreasing with respect to the origin in <span>(B_1(0))</span> for any <span>(tin mathbb {R})</span>. Another one is to establish the Liouville theorem for homogeneous master equation </p><span>$$begin{aligned} (partial _t-Delta )^s u(x,t)=0 ,,, text{ in },, mathbb {R}^ntimes mathbb {R}, end{aligned}$$</span><p>which states that all bounded solutions must be constant. We propose a new methodology for a direct method of moving planes applicable to the fully fractional heat operator <span>((partial _t-Delta )^s)</span>, and the proof of our main results based on this direct method involves the perturbation technique, limit argument as well as Fourier transform. This study opens up a way to investigate the geometric behavior of master equations, and provides valuable insights for establishing qualitative properties of solutions and even for deriving important Liouville theorems for other types of fractional order parabolic equations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"16 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141974003","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
The McKay $$I_nu $$ Bessel distribution revisited 麦凯 $$I_nu $$ 贝塞尔分布再探讨
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-09 DOI: 10.1007/s13540-024-00322-z
Dragana Jankov Maširević
{"title":"The McKay $$I_nu $$ Bessel distribution revisited","authors":"Dragana Jankov Maširević","doi":"10.1007/s13540-024-00322-z","DOIUrl":"https://doi.org/10.1007/s13540-024-00322-z","url":null,"abstract":"<p>Bearing in mind an increasing popularity of the fractional calculus the main aim of this paper is to derive several new representation formulae for the cumulative distribution function (cdf) of the McKay <span>(I_nu )</span> Bessel distribution including the Grünwald-Letnikov fractional derivative; also, two connection formulae between cdf of the McKay <span>(I_nu )</span> random variable and the so–called Neumann series of modified Bessel functions of the first kind are established, providing, consequently, a new integral representation for such cdf in terms of a definite integral. Another fashion expression for the given cdf is derived in terms of the Grünwald-Letnikov fractional derivative of the widely applicable Marcum Q–function, which represents a certain simplification of the already existing relationship between McKay <span>(I_nu )</span> random variable and a Marcum Q–functions. The exposition ends with some open questions, drawing the interested reader’s attention, among others, to the summation of some Neumann series.\u0000</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"21 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910463","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 boundary value problems and elastic sticky brownian motions 分数边界值问题和弹性粘性布朗运动
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-09 DOI: 10.1007/s13540-024-00313-0
Mirko D’Ovidio
{"title":"Fractional boundary value problems and elastic sticky brownian motions","authors":"Mirko D’Ovidio","doi":"10.1007/s13540-024-00313-0","DOIUrl":"https://doi.org/10.1007/s13540-024-00313-0","url":null,"abstract":"<p>We extend the results obtained in [14] by introducing a new class of boundary value problems involving non-local dynamic boundary conditions. We focus on the problem to find a solution to a local problem on a domain <span>(varOmega )</span> with non-local dynamic conditions on the boundary <span>(partial varOmega )</span>. Due to the pioneering nature of the present research, we propose here the apparently simple case of <span>(varOmega =(0, infty ))</span> with boundary <span>({0})</span> of zero Lebesgue measure. Our results turn out to be instructive for the general case of boundary with positive (finite) Borel measures. Moreover, in our view, we bring new light to dynamic boundary value problems and the probabilistic description of the associated models.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"50 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910464","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
On the existence and uniqueness of the solution to multifractional stochastic delay differential equation 论多分数随机延迟微分方程解的存在性和唯一性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-09 DOI: 10.1007/s13540-024-00314-z
Khaoula Bouguetof, Zaineb Mezdoud, Omar Kebiri, Carsten Hartmann
{"title":"On the existence and uniqueness of the solution to multifractional stochastic delay differential equation","authors":"Khaoula Bouguetof, Zaineb Mezdoud, Omar Kebiri, Carsten Hartmann","doi":"10.1007/s13540-024-00314-z","DOIUrl":"https://doi.org/10.1007/s13540-024-00314-z","url":null,"abstract":"<p>In this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"102 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910462","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
Mixed fractional stochastic heat equation with additive fractional-colored noise 带有加性分数色噪声的混合分数随机热方程
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-08-08 DOI: 10.1007/s13540-024-00317-w
Eya Zougar
{"title":"Mixed fractional stochastic heat equation with additive fractional-colored noise","authors":"Eya Zougar","doi":"10.1007/s13540-024-00317-w","DOIUrl":"https://doi.org/10.1007/s13540-024-00317-w","url":null,"abstract":"<p>We investigate the fractional stochastic heat equation, driven by a random noise which admits a covariance measure structure with respect to the time variable and has a spatial covariance given by the Riesz kernel. This class of process includes White-colored noise, fractional colored noise and other related processes. We give a sufficient condition for the existence of the mild solution and we establish some properties of its. Then, we study the self similarity and the path regularity of this solution with respect to time variable on the particular case when the noise behaves as a fractional Brownian motion in time.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"30 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141909283","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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