发布求助
文献互助 智能选刊 最新文献

Fractional Calculus and Applied Analysis最新文献

筛选
英文 中文
On variable-order fractional linear viscoelasticity 关于变阶分数线性粘弹性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-13 DOI: 10.1007/s13540-024-00288-y
Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli
{"title":"On variable-order fractional linear viscoelasticity","authors":"Andrea Giusti, Ivano Colombaro, Roberto Garra, Roberto Garrappa, Andrea Mentrelli","doi":"10.1007/s13540-024-00288-y","DOIUrl":"https://doi.org/10.1007/s13540-024-00288-y","url":null,"abstract":"<p>A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a <i>variable-order fractional Maxwell model</i> is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140919789","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
Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes 由 Dickman 下位器和相关随机过程生成的广义分数导数
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-10 DOI: 10.1007/s13540-024-00289-x
Neha Gupta, Arun Kumar, Nikolai Leonenko, Jayme Vaz
{"title":"Generalized fractional derivatives generated by Dickman subordinator and related stochastic processes","authors":"Neha Gupta, Arun Kumar, Nikolai Leonenko, Jayme Vaz","doi":"10.1007/s13540-024-00289-x","DOIUrl":"https://doi.org/10.1007/s13540-024-00289-x","url":null,"abstract":"<p>In this article, convolution-type fractional derivatives generated by Dickman subordinator and inverse Dickman subordinator are discussed. The Dickman subordinator and its inverse are generalizations of stable and inverse stable subordinators, respectively. The series representations of densities of the Dickman subordinator and inverse Dickman subordinator are also obtained, which could be helpful for computational purposes. Moreover, the space and time-fractional Poisson-Dickman processes, space-fractional Skellam Dickman process and non-homogenous Poisson-Dickman process are introduced and their main properties are studied.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140907414","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
Well-posedness and stability of a fractional heat-conductor with fading memory 具有褪色记忆的分数热导体的良好假设性和稳定性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-10 DOI: 10.1007/s13540-024-00291-3
Sebti Kerbal, Nasser-eddine Tatar, Nasser Al-Salti
{"title":"Well-posedness and stability of a fractional heat-conductor with fading memory","authors":"Sebti Kerbal, Nasser-eddine Tatar, Nasser Al-Salti","doi":"10.1007/s13540-024-00291-3","DOIUrl":"https://doi.org/10.1007/s13540-024-00291-3","url":null,"abstract":"<p>We consider a problem which describes the heat diffusion in a complex media with fading memory. The model involves a fractional time derivative of order between zero and one instead of the classical first order derivative. The model takes into account also the effect of a neutral delay. We discuss the existence and uniqueness of a mild solution as well as a classical solution. Then, we prove a Mittag-Leffler stability result. Unlike the integer-order case, we run into considerable difficulties when estimating some problematic terms. It is found that even without the memory term in the heat flux expression, the stability is still of Mittag-Leffler type.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140907415","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 convergence of the Galerkin method for random fractional differential equations 论随机分数微分方程伽勒金方法的收敛性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-06 DOI: 10.1007/s13540-024-00287-z
Marc Jornet
{"title":"On the convergence of the Galerkin method for random fractional differential equations","authors":"Marc Jornet","doi":"10.1007/s13540-024-00287-z","DOIUrl":"https://doi.org/10.1007/s13540-024-00287-z","url":null,"abstract":"<p>In the context of forward uncertainty quantification, we investigate the convergence of the Galerkin projections for random fractional differential equations. The governing system is formed by a finite set of independent input random parameters (a germ) and by a fractional derivative in the Caputo sense. Input uncertainty arises from biased measurements, and a fractional derivative, defined by a convolution, takes past history into account. While numerical experiments on the gPC-based Galerkin method are already available in the literature for random ordinary, partial and fractional differential equations, a theoretical analysis of mean-square convergence is still lacking for the fractional case. The aim of this contribution is to fill this gap, by establishing new inequalities and results and by raising new open problems.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140895882","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 and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces 巴拿赫空间中非线性分数超扩散方程后向问题温和解的存在性与正则性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-06 DOI: 10.1007/s13540-024-00286-0
Xuan X. Xi, Yong Zhou, Mimi Hou
{"title":"Existence and regularity of mild solutions to backward problem for nonlinear fractional super-diffusion equations in Banach spaces","authors":"Xuan X. Xi, Yong Zhou, Mimi Hou","doi":"10.1007/s13540-024-00286-0","DOIUrl":"https://doi.org/10.1007/s13540-024-00286-0","url":null,"abstract":"<p>In this paper, we study a class of backward problems for nonlinear fractional super-diffusion equations in Banach spaces. We consider the time fractional derivative in the sense of Caputo type. First, we establish some results for the existence of the mild solutions. Moreover, we obtain regularity results of the first order and fractional derivatives of mild solutions. These conclusions are mainly based on fixed point theorems and properties of <span>(alpha )</span>-resolvent family as well as Mittag-Leffler functions. Finally, two applications are provided to illustrate the efficiency of our results.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140895819","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Author Correction: On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications 作者更正：关于各向异性变指数索波列夫空间的集中-紧凑性原理及其应用
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-04-17 DOI: 10.1007/s13540-024-00282-4
Nabil Chems Eddine, M. Ragusa, D. D. Repovš
{"title":"Author Correction: On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications","authors":"Nabil Chems Eddine, M. Ragusa, D. D. Repovš","doi":"10.1007/s13540-024-00282-4","DOIUrl":"https://doi.org/10.1007/s13540-024-00282-4","url":null,"abstract":"","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140691203","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":null,"pages":null},"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信