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Fractional Calculus and Applied Analysis最新文献

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On fractional differential inclusion with damping driven by variational-hemivariational inequality
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-29 DOI: 10.1007/s13540-025-00375-8
Yunshui Liang, Lu-Chuan Ceng, Shengda Zeng
{"title":"On fractional differential inclusion with damping driven by variational-hemivariational inequality","authors":"Yunshui Liang, Lu-Chuan Ceng, Shengda Zeng","doi":"10.1007/s13540-025-00375-8","DOIUrl":"https://doi.org/10.1007/s13540-025-00375-8","url":null,"abstract":"<p>In this paper we study an evolution problem (FDIVHVI) which constitutes of the nonlinear fractional differential inclusion with damping driven by a variational-hemivariational inequality (VHVI) in Banach spaces. More precisely, first, it is shown that the solution set for VHVI is nonempty, bounded, convex and closed under the surjectivity theorem and the Minty formula. Then, we introduce an associated multivalued map with the solution set of the VHVI, and prove that it is upper semicontinuous and measurable. Finally, by utilizing the fixed point theorem of condensing multivalued operators, properties of <span>((alpha , mu ))</span>-regularized families of operators and properties of measure of noncompactness, we show the existence of mild solutions for FDIVHVI.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"66 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056989","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 a uniqueness criterion for nonlinear fractional differential equations
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-24 DOI: 10.1007/s13540-025-00374-9
Nguyen Minh Dien
{"title":"On a uniqueness criterion for nonlinear fractional differential equations","authors":"Nguyen Minh Dien","doi":"10.1007/s13540-025-00374-9","DOIUrl":"https://doi.org/10.1007/s13540-025-00374-9","url":null,"abstract":"<p>In this note, we present a new uniqueness criterion for nonlinear fractional differential equations, which can be seen as an improvement of the result given by Ferreira [Bull. London Math. Soc. <b>45</b>, 930–934 (2013)].</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"35 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143030931","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
Cauchy problem for time-space fractional incompressible Navier-Stokes equations in $$mathbb {R}^n$$ 时空分式不可压缩Navier-Stokes方程的Cauchy问题 $$mathbb {R}^n$$
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-21 DOI: 10.1007/s13540-025-00373-w
Miao Yang, Li-Zhen Wang, Lu-Sheng Wang
{"title":"Cauchy problem for time-space fractional incompressible Navier-Stokes equations in $$mathbb {R}^n$$","authors":"Miao Yang, Li-Zhen Wang, Lu-Sheng Wang","doi":"10.1007/s13540-025-00373-w","DOIUrl":"https://doi.org/10.1007/s13540-025-00373-w","url":null,"abstract":"<p>In this paper, Cauchy problem for incompressible Navier-Stokes equations with time fractional differential operator and fractional Laplacian in <span>(mathbb {R}^n)</span> (<span>(nge 2)</span>) is investigated. The global and local existence and uniqueness of mild solutions are obtained with the help of Banach fixed point theorem when the initial data belongs to <span>(L^{p_{c}}(mathbb {R}^n))</span> <span>((p_c=frac{n}{alpha -1}))</span>. In addition, the decay properties of mild solutions to the considered time-space fractional equations are constructed. Moreover, it is shown that when the initial data belongs to <span>(L^{p_{c}}(mathbb {R}^n)cap L^{p}(mathbb {R}^n))</span> with <span>(1&lt;p&lt;p_c)</span>, the existence and uniqueness of global and local mild solutions can also be established. At the end of this paper, the integrability of mild solutions is discussed.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"33 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142992757","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 approximate controllability of Hilfer fractional impulsive evolution equations Hilfer分数阶脉冲演化方程的存在性及近似可控性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-17 DOI: 10.1007/s13540-025-00372-x
Kee Qiu, Michal Fečkan, JinRong Wang
{"title":"Existence and approximate controllability of Hilfer fractional impulsive evolution equations","authors":"Kee Qiu, Michal Fečkan, JinRong Wang","doi":"10.1007/s13540-025-00372-x","DOIUrl":"https://doi.org/10.1007/s13540-025-00372-x","url":null,"abstract":"<p>Our main concern is the existence of a new <span>(PC_{2-v})</span>-mild solution for Hilfer fractional impulsive evolution equations of order <span>(alpha in (1,2))</span> and <span>(beta in [0,1])</span> as well as the approximate controllability problem in Banach spaces. Firstly, under the condition that the operator <i>A</i> is the infinitesimal generator of a cosine family, we give a new representation of <span>(PC_{2-v})</span>-mild solution for the objective equations by the Laplace transform and probability density function. Secondly, we rely on the Banach contraction mapping principle to discuss a new existence and uniqueness result of <span>(PC_{2-v})</span>-mild solution when the sine family is compact. Thirdly, a sufficient condition for the approximate controllability result of impulsive evolution equations is formulated and proved under the assumptions that the nonlinear item is uniformly bounded and the corresponding fractional linear system is approximately controllable. Finally, two examples are given to illustrate the validity of the obtained results in the application.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"97 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989302","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 slow-fast stochastic differential equations: Averaging principle result 混合慢快随机微分方程：平均原理结果
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-17 DOI: 10.1007/s13540-024-00368-z
Shitao Liu
{"title":"Mixed slow-fast stochastic differential equations: Averaging principle result","authors":"Shitao Liu","doi":"10.1007/s13540-024-00368-z","DOIUrl":"https://doi.org/10.1007/s13540-024-00368-z","url":null,"abstract":"<p>This paper investigates stochastic averaging principle for a class of mixed slow-fast stochastic differential equations driven simultaneously by a multidimensional standard Brownian motion and a multidimensional fractional Brownian motion with Hurst parameter <span>(1/2&lt;H&lt;1)</span>. The stochastic averaging principle shows that the slow component strongly converges to the solution of the corresponding averaged equations under a weaker condition than the Lipschitz one.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"7 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989253","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 quasi-reversibility method for recovering a source in a fractional evolution equation 分数阶演化方程中恢复源的准可逆性方法
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-17 DOI: 10.1007/s13540-025-00370-z
Liangliang Sun, Zhaoqi Zhang, Yunxin Wang
{"title":"The quasi-reversibility method for recovering a source in a fractional evolution equation","authors":"Liangliang Sun, Zhaoqi Zhang, Yunxin Wang","doi":"10.1007/s13540-025-00370-z","DOIUrl":"https://doi.org/10.1007/s13540-025-00370-z","url":null,"abstract":"<p>In this paper, a quasi-reversibility method is used to solve an inverse spatial source problem of multi-term time-space fractional parabolic equation by observation at the terminal measurement data. We are mainly concerned with the case where the time source can be changed sign, which is practically important but has not been well explored in literature. Under certain conditions on the time source, we establish the uniqueness of the inverse problem, and also a Hölder-type conditional stability of the inverse problem is firstly given. Meanwhile, we prove a stability estimate of optimal order for the inverse problem. Then some convergence estimates for the regularized solution are proved under an a-priori and an a-posteriori regularization parameter choice rule. Finally, several numerical experiments illustrate the effectiveness of the proposed method in one-dimensional case.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"44 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989254","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
An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity 具有初始奇异性的非线性分数阶微分方程的改进分数阶预测-校正方法
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-17 DOI: 10.1007/s13540-025-00371-y
Jianfei Huang, Junlan Lv, Sadia Arshad
{"title":"An improved fractional predictor-corrector method for nonlinear fractional differential equations with initial singularity","authors":"Jianfei Huang, Junlan Lv, Sadia Arshad","doi":"10.1007/s13540-025-00371-y","DOIUrl":"https://doi.org/10.1007/s13540-025-00371-y","url":null,"abstract":"<p>The solution and source term of nonlinear fractional differential equations (NFDEs) with initial values generally have the initial singularity. As is known that numerical methods for NFDEs usually occur the phenomenon of order reduction due to the existence of initial singularity. In this paper, an improved fractional predictor-corrector (PC) method is developed for NFDEs based on the technique of variable transformation. This improved fractional PC method can achieve the optimal convergence order, i.e., the <span>(1+alpha )</span> order convergence rate for fractional order <span>(alpha in (0,1))</span>, of the classical fractional PC method under the high smoothness requirement on the solution and source term. Furthermore, the detailed error analysis also exhibits the relationship between the convergence rate of the improved fractional PC method and the regularities of the solution and source term. Finally, the theoretical error estimate is verified through numerical experiments.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"56 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989252","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 uniqueness of discrete weighted pseudo S-asymptotically $$omega $$ -periodic solution to abstract semilinear superdiffusive difference equation 抽象半线性超扩散差分方程离散加权伪s渐近$$omega $$周期解的存在唯一性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-07 DOI: 10.1007/s13540-024-00366-1
Jorge González-Camus
{"title":"Existence and uniqueness of discrete weighted pseudo S-asymptotically $$omega $$ -periodic solution to abstract semilinear superdiffusive difference equation","authors":"Jorge González-Camus","doi":"10.1007/s13540-024-00366-1","DOIUrl":"https://doi.org/10.1007/s13540-024-00366-1","url":null,"abstract":"<p>In this paper, we establish sufficient conditions in order to guarantee the existence and uniqueness of discrete weighted pseudo <i>S</i>-asymptotically <span>(omega )</span>-periodic solution to the semilinear fractional difference equation </p><span>$$begin{aligned} {left{ begin{array}{ll} _Cnabla ^{alpha } u^n=Au^n+g^n(u^n), quad nge 2, u^0=x_0 in X, quad u^1=x_1in X, end{array}right. } end{aligned}$$</span><p>where <span>(1&lt;alpha &lt;2,)</span> <i>A</i> is a closed linear operator in a Banach space <i>X</i> which generates an <span>((alpha ,beta ))</span>-resolvent sequence <span>({S^n_{alpha ,beta }}_{nin mathbb N_0}subset mathcal {B}(X))</span> and <span>(g:mathbb N_0times Xrightarrow X)</span> a discrete weighted pseudo <i>S</i>-asymptotically <span>(omega )</span>-periodic function satisfying suitable Lipschitz type conditions in the spatial variable (local and global), based in fixed point Theorems. In order to achieve this objective, we prove invariance by convolution and principle of superposition for a class of suitables function spaces.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"29 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935720","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 solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions 具有初始非局部和积分超定条件的分数阶扩散方程反系数问题的全局可解性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-07 DOI: 10.1007/s13540-024-00367-0
Durdimurod Durdiev, Askar Rahmonov
{"title":"Global solvability of inverse coefficient problem for one fractional diffusion equation with initial non-local and integral overdetermination conditions","authors":"Durdimurod Durdiev, Askar Rahmonov","doi":"10.1007/s13540-024-00367-0","DOIUrl":"https://doi.org/10.1007/s13540-024-00367-0","url":null,"abstract":"<p>In this work, we consider an inverse problem of determining the coefficient at the lower term of a fractional diffusion equation. The direct problem is the initial-boundary problem for this equation with non-local initial and homogeneous Dirichlet conditions. To determine the unknown coefficient, an overdetermination condition of the integral form is specified with respect to the solution of the direct problem. Using Green’s function for an ordinary fractional differential equation with a non-local boundary condition and the Fourier method, the inverse problem is reduced to an equivalent problem. Further, by using the fixed-point argument in suitable Sobolev spaces, the global theorems of existence and uniqueness for the solution of the inverse problem are obtained.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"35 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142935721","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
Continuity of solutions for tempered fractional general diffusion equations driven by TFBM TFBM驱动的回火分数阶一般扩散方程解的连续性
IF 3 2区 数学
Fractional Calculus and Applied Analysis Pub Date : 2025-01-03 DOI: 10.1007/s13540-024-00369-y
Lijuan Zhang, Yejuan Wang
{"title":"Continuity of solutions for tempered fractional general diffusion equations driven by TFBM","authors":"Lijuan Zhang, Yejuan Wang","doi":"10.1007/s13540-024-00369-y","DOIUrl":"https://doi.org/10.1007/s13540-024-00369-y","url":null,"abstract":"<p>This paper is devoted to the continuity of the weak solution for tempered fractional general diffusion equations driven by tempered fractional Brownian motion (TFBM). Based on the Feynman-Kac formula (1.2), by using the Itô isometry for the stochastic integral with respect to TFBM, Parseval’s identity and some ingenious calculations, we establish the continuities of the solution with respect to Hurst index <i>H</i> and tempering parameter <span>(lambda )</span> of TFBM.</p>","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"20 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142924653","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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