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Fractional Calculus and Applied Analysis最新文献

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On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases 关于一类非线性分数薛定谔-泊松系统解的存在性：亚临界和临界情况
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-06-03 DOI: 10.1007/s13540-024-00296-y
Lin Li, Huo Tao, Stepan Tersian
{"title":"On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases","authors":"Lin Li, Huo Tao, Stepan Tersian","doi":"10.1007/s13540-024-00296-y","DOIUrl":"https://doi.org/10.1007/s13540-024-00296-y","url":null,"abstract":"<p>In this paper, we establish the existence of standing wave solutions for a class of nonlinear fractional Schrödinger-Poisson system involving nonlinearity with subcritical and critical growth. We suppose that the potential <i>V</i> satisfies either Palais-Smale type condition or there exists a bounded domain <span>(varOmega )</span> such that <i>V</i> has no critical point in <span>(partial varOmega )</span>. To overcome the “lack of compactness\" of the problem, we combine Del Pino-Felmer’s penalization technique with Moser’s iteration method and some ideas from Alves [1].</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"42 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141235827","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
Stability analysis of discrete-time tempered fractional-order neural networks with time delays 带时间延迟的离散时间节制分数阶神经网络的稳定性分析
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-30 DOI: 10.1007/s13540-024-00295-z
Xiao-Li Zhang, Yongguang Yu, Hu Wang, Jiahui Feng
{"title":"Stability analysis of discrete-time tempered fractional-order neural networks with time delays","authors":"Xiao-Li Zhang, Yongguang Yu, Hu Wang, Jiahui Feng","doi":"10.1007/s13540-024-00295-z","DOIUrl":"https://doi.org/10.1007/s13540-024-00295-z","url":null,"abstract":"<p>In order to accurately capture non-local properties and long-term memory effects, this study combines the tempered fractional-order operator with delayed neural networks to investigate its stability, leveraging the introduced decay term of the tempered fractional-order operator. Firstly, the discrete-time tempered fractional-order neural networks model (DTFNNs) is presented. Furthermore, in an effort to better understand the dynamic behavior of complex systems, solutions to discrete-time tempered fractional non-homogeneous equations are obtained. The stability conditions for systems are subsequently established, contributing novel insights to the field. To validate the robustness of these conditions, numerical experiments are conducted, underscoring the practical relevance of the proposed model.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"69 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141182381","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 equations of Bagley-Torvik and Langevin type Bagley-Torvik 和 Langevin 型微分方程
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-23 DOI: 10.1007/s13540-024-00292-2
J. R. L. Webb, Kunquan Lan
{"title":"Fractional differential equations of Bagley-Torvik and Langevin type","authors":"J. R. L. Webb, Kunquan Lan","doi":"10.1007/s13540-024-00292-2","DOIUrl":"https://doi.org/10.1007/s13540-024-00292-2","url":null,"abstract":"<p>Nonlinear fractional equations for Caputo differential operators with two fractional orders are studied. One case is a generalization of the Bagley-Torvik equation, another is of Langevin type. These can be confused as being the same but because fractional derivatives do not commute these are different problems. However it is possible to use some common methodology. Some new regularity results for fractional integrals of a certain type are proved. These are used to rigorously prove equivalences between solutions of initial value problems for the fractional derivative equations and solutions of the corresponding integral equations in the space of continuous functions. A novelty is that it is not assumed that the nonlinear term is continuous but that it satisfies the weaker <span>(L^{p})</span>-Carathéodory condition. Existence of solutions on an interval [0, <i>T</i>] in cases where <i>T</i> can be arbitrarily large, so-called global solutions, are proved, obtaining the necessary <i>a priori</i> bounds by using recent fractional Gronwall and fractional Bihari inequalities.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"14 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091909","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
Principal curves to fractional m-Laplacian systems and related maximum and comparison principles 分数 m-Laplacian 系统的主曲线及相关的最大值和比较原则
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-20 DOI: 10.1007/s13540-024-00293-1
Anderson L. A. de Araujo, Edir J. F. Leite, Aldo H. S. Medeiros
{"title":"Principal curves to fractional m-Laplacian systems and related maximum and comparison principles","authors":"Anderson L. A. de Araujo, Edir J. F. Leite, Aldo H. S. Medeiros","doi":"10.1007/s13540-024-00293-1","DOIUrl":"https://doi.org/10.1007/s13540-024-00293-1","url":null,"abstract":"<p>In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional <i>m</i>-Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of bounded domain <span>(varOmega subset {mathbb {R}}^N)</span> are also proved. As application, we measure explicitly how small has to be <span>(text {diam}(varOmega ))</span> so that weak and strong maximum principles associated to this problem hold in <span>(varOmega )</span>.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"411 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141074222","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
Pricing European option under the generalized fractional jump-diffusion model 广义分数跳跃扩散模型下的欧式期权定价
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2024-05-16 DOI: 10.1007/s13540-024-00290-4
Jingjun Guo, Yubing Wang, Weiyi Kang
{"title":"Pricing European option under the generalized fractional jump-diffusion model","authors":"Jingjun Guo, Yubing Wang, Weiyi Kang","doi":"10.1007/s13540-024-00290-4","DOIUrl":"https://doi.org/10.1007/s13540-024-00290-4","url":null,"abstract":"<p>The pricing problem of European option is investigated under the generalized fractional jump-diffusion model. First of all, the generalized fractional jump-diffusion model is proposed, with the assumption that the underlying asset price follows this model, and the explicit solution is derived using the Itô formula. Then, the partial differential equation (PDE) of the European option price is obtained by using the delta-hedging strategy, and the analytical solutions of the European call and put option prices are obtained through the risk-neutral pricing principle. Moreover, the accuracy of closed-form formula for European option pricing is verified by the Monte Carlo simulation. Furthermore, the properties of the pricing formulas are discussed and the impact of main parameters on the option pricing model are analyzed via calculations of Greeks. Finally, the rationality and validity of the established option pricing model are verified by numerical analysis.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"25 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140953472","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 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":"153 1","pages":""},"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":"31 1","pages":""},"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":"64 1","pages":""},"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":"32 1","pages":""},"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":"14 1","pages":""},"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
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