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Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable 具有周期性依赖于空间变量非线性的分数阶非线性Schrödinger方程的不变环面
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-05-05 DOI: 10.1007/s13540-025-00409-1
Jieyu Liu, Jing Zhang
{"title":"Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable","authors":"Jieyu Liu, Jing Zhang","doi":"10.1007/s13540-025-00409-1","DOIUrl":"https://doi.org/10.1007/s13540-025-00409-1","url":null,"abstract":"<p>In this paper, we focus on a type of fractional nonlinear Schrödinger equation with odd periodic boundary conditions, where the nonlinearity periodically depending on spatial variable <i>x</i>. By an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible systems with unbounded perturbation, we obtain that there exists a lot of smooth quasi-periodic solutions with small amplitude for fractional nonlinear Schrödinger equations.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"35 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143910700","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, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian 与分数阶拉普拉斯算子相关的非线性BVP有界解的存在性、不存在性和多重性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-05-05 DOI: 10.1007/s13540-025-00410-8
José Carmona Tapia, Rubén Fiñana Aránega
{"title":"Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian","authors":"José Carmona Tapia, Rubén Fiñana Aránega","doi":"10.1007/s13540-025-00410-8","DOIUrl":"https://doi.org/10.1007/s13540-025-00410-8","url":null,"abstract":"<p>We deal with the boundary value problem </p><span>$$begin{aligned} {left{ begin{array}{ll} (-Delta )^s u(x)= lambda f(u(x)), &amp; xin Omega , u(x)=0, &amp; xin mathbb {R}^N setminus Omega , end{array}right. } end{aligned}$$</span><p>where <span>(Omega )</span> is an open and bounded subset of <span>(mathbb {R}^N)</span> with smooth boundary, <span>((-Delta )^s)</span>, <span>(sin (0,1))</span> denotes the fractional Laplacian, <span>(lambda ge 0)</span> and <i>f</i> is locally Lipschitz and continuous. We provide necessary and sufficient conditions on <i>f</i> to ensure existence and multiplicity of bounded solutions between two zeros of <i>f</i>.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"26 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143910699","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 local and nonlocal eigenvalue problems in the exterior domain 外域的混合局部和非局部特征值问题
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-05-05 DOI: 10.1007/s13540-025-00416-2
R. Lakshmi, Sekhar Ghosh
{"title":"Mixed local and nonlocal eigenvalue problems in the exterior domain","authors":"R. Lakshmi, Sekhar Ghosh","doi":"10.1007/s13540-025-00416-2","DOIUrl":"https://doi.org/10.1007/s13540-025-00416-2","url":null,"abstract":"<p>This paper aims to study the eigenvalue problems of a mixed local and nonlocal operator in the exterior of a nonempty, bounded, simply connected domain <span>(varOmega subset {mathbb {R}}^N)</span> with Lipschitz boundary <span>(partial varOmega ne emptyset )</span>. By employing the variational methods combined with the <i>Ljusternik-Schnirelmann principle</i>, we prove the existence of a non-decreasing sequence of eigenvalues. In particular, we prove the principal eigenvalue is simple and isolated. We establish the positivity of the first eigenfunction by obtaining a strong maximum principle. The results obtained here are new even for the case <span>(p=2)</span>.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"282 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143910698","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
Inverse coefficient problems for the heat equation with fractional Laplacian 分数阶拉普拉斯热方程的反系数问题
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-05-02 DOI: 10.1007/s13540-025-00414-4
Azizbek Mamanazarov, Durvudkhan Suragan
{"title":"Inverse coefficient problems for the heat equation with fractional Laplacian","authors":"Azizbek Mamanazarov, Durvudkhan Suragan","doi":"10.1007/s13540-025-00414-4","DOIUrl":"https://doi.org/10.1007/s13540-025-00414-4","url":null,"abstract":"<p>In the present paper, we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point ensures the existence of a weak solution for the inverse problem. Furthermore, if there is an additional datum at the observation point, it leads to a specific formula for the time-dependent source coefficient. Moreover, we investigate inverse problems involving non-local data of the fractional heat equation.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"14 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898233","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
Ground state solution for a generalized Choquard Schr $$ddot{text {o}}$$ dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces 齐次分数型Musielak Sobolev空间中具有消失势的广义Choquard Schr $$ddot{text {o}}$$ dinger方程的基态解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-05-01 DOI: 10.1007/s13540-025-00411-7
Shilpa Gupta, Gaurav Dwivedi
{"title":"Ground state solution for a generalized Choquard Schr $$ddot{text {o}}$$ dinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces","authors":"Shilpa Gupta, Gaurav Dwivedi","doi":"10.1007/s13540-025-00411-7","DOIUrl":"https://doi.org/10.1007/s13540-025-00411-7","url":null,"abstract":"<p>This paper aims to establish the existence of a weak solution for the following problem: </p><span>$$begin{aligned} (-Delta )^{s}_{mathcal {H}}u(x) +V(x)h(x,x,|u|)u(x)=left( int _{{mathbb R}^{N}}dfrac{K(y)F(u(y))}{|x-y|^lambda },textrm{d}yright) K(x)f(u(x)), end{aligned}$$</span><p>in <span>({mathbb R}^{N})</span> where <span>(Nge 1)</span>, <span>(sin (0,1), lambda in (0,N), mathcal {H}(x,y,t)=int _{0}^{|t|} h(x,y,r)r dr,)</span> <span>( h:{mathbb R}^{N}times {mathbb R}^{N}times [0,infty )rightarrow [0,infty ))</span> is a generalized <i>N</i>-function and <span>((-Delta )^{s}_{mathcal {H}})</span> is a generalized fractional Laplace operator. The functions <span>(V,K:{mathbb R}^{N}rightarrow (0,infty ))</span>, non-linear function <span>(f:{mathbb R}rightarrow {mathbb R})</span> are continuous and <span>( F(t)=int _{0}^{t}f(r)dr.)</span> First, we introduce the homogeneous fractional Musielak–Sobolev space and investigate their properties. After that, we pose the given problem in that space. To establish our existence results, we use variational technique based on the mountain pass theorem. We also prove the existence of a ground state solution by the method of Nehari manifold.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"4 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894041","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 solutions of fractional nonlinear Fokker-Planck equation 分数阶非线性Fokker-Planck方程的解
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-30 DOI: 10.1007/s13540-025-00413-5
Komal Singla, Nikolai Leonenko
{"title":"On solutions of fractional nonlinear Fokker-Planck equation","authors":"Komal Singla, Nikolai Leonenko","doi":"10.1007/s13540-025-00413-5","DOIUrl":"https://doi.org/10.1007/s13540-025-00413-5","url":null,"abstract":"<p>In this work, the exact solutions of time fractional Fokker-Planck equation are investigated using the symmetry approach. Also, the convergence of the reported solutions is proved along with the graphical interpretation of the obtained solutions.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"34 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889472","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 nonlinear fractional Rayleigh-Stokes problem on an infinite interval 无穷区间上的非线性分数型Rayleigh-Stokes问题
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-29 DOI: 10.1007/s13540-025-00408-2
Jing Na Wang
{"title":"The nonlinear fractional Rayleigh-Stokes problem on an infinite interval","authors":"Jing Na Wang","doi":"10.1007/s13540-025-00408-2","DOIUrl":"https://doi.org/10.1007/s13540-025-00408-2","url":null,"abstract":"<p>In this paper, we investigate the existence of mild solutions of the nonlinear fractional Rayleigh-Stokes problem for a generalized second grade fluid on an infinite interval. We firstly show the boundedness and continuity of solution operator. And then, by using a generalized Arzelà-Ascoli theorem and some new techniques, we get the compactness on the infinite interval. Moreover, we prove the existence of global mild solutions of nonlinear fractional Rayleigh-Stokes problem.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"34 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889704","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
Solvability for a class of two-term nonlinear functional boundary value problems and its applications 一类两项非线性泛函边值问题的可解性及其应用
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-29 DOI: 10.1007/s13540-025-00407-3
Bingzhi Sun, Shuqin Zhang, Dongyu Yang
{"title":"Solvability for a class of two-term nonlinear functional boundary value problems and its applications","authors":"Bingzhi Sun, Shuqin Zhang, Dongyu Yang","doi":"10.1007/s13540-025-00407-3","DOIUrl":"https://doi.org/10.1007/s13540-025-00407-3","url":null,"abstract":"<p>In this paper, we are concerned with a two-term fractional differential equation with functional boundary conditions. We discuss the existence of two kinds of solutions with respect to this type of equation. In this sense, for a class of two-term problems with specific boundary conditions, we use Matlab software to calculate the eigenvalues of the boundary value problems with Riemann-Liouville fractional derivative as an application of the two-term fractional differential equation, and further, we derive the dependence of eigenvalues on some parameters. Finally, we indicate that this method of estimating the eigenvalues by means of such two-term fractional order equations will also help in solving other eigenvalue problems.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"43 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889572","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
Multiplicity of couple solution for a fractional $$(varphi , psi )$$ -like system 分数阶$$(varphi , psi )$$类系统耦合解的多重性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-29 DOI: 10.1007/s13540-025-00412-6
Abderrahmane Lakhdari, Chaima Nefzi
{"title":"Multiplicity of couple solution for a fractional $$(varphi , psi )$$ -like system","authors":"Abderrahmane Lakhdari, Chaima Nefzi","doi":"10.1007/s13540-025-00412-6","DOIUrl":"https://doi.org/10.1007/s13540-025-00412-6","url":null,"abstract":"<p>This paper delves into the existence of three weak solutions for a fractional <span>((varphi , psi ))</span>-like system involving the fractional <span>(varphi )</span> Laplacian and the fractional <span>(psi )</span> Laplacian respectively within the fractional Orlicz-Sobolev space. The proof is achieved by the well-known Bonanno-Marano techniques.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"70 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143889471","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
Harnack inequalities for functional SDEs driven by fractional Ornstein-Uhlenbeck process 分数阶Ornstein-Uhlenbeck过程驱动的泛函SDEs的Harnack不等式
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-04-22 DOI: 10.1007/s13540-025-00399-0
Zhi Li, Meiqian Liu, Liping Xu
{"title":"Harnack inequalities for functional SDEs driven by fractional Ornstein-Uhlenbeck process","authors":"Zhi Li, Meiqian Liu, Liping Xu","doi":"10.1007/s13540-025-00399-0","DOIUrl":"https://doi.org/10.1007/s13540-025-00399-0","url":null,"abstract":"<p>Being based on coupling by change of measure and an approximation technique, the Harnack inequalities for a class of stochastic functional differential equations driven by fractional Ornstein-Uhlenbeck process with Hurst parameter <span>(0&lt;H&lt;1/2)</span> are established. By using a transformation formulas for fractional Brownian motion, the Harnack inequalities for stochastic functional differential equations driven by fractional Ornstein-Uhlenbeck process with Hurst parameter <span>(1/2&lt;H&lt;1)</span> are established.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"13 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143862867","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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