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Fractional Differential Calculus最新文献

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On controllability of linear and nonlinear fractional integrodifferential systems 线性和非线性分数阶积分微分系统的可控性
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/FDC-2019-09-02
M. Matar
{"title":"On controllability of linear and nonlinear fractional integrodifferential systems","authors":"M. Matar","doi":"10.7153/FDC-2019-09-02","DOIUrl":"https://doi.org/10.7153/FDC-2019-09-02","url":null,"abstract":". In this article we investigate the controllability problem of linear and nonlinear frac- tional integrodifferential systems. We justify the controllability concepts on a fractional integrodifferential linear system, and use results, as well as Schauder’s fi xed point theorem, to obtain the controllability of the corresponding nonlinear system. Some applications are introduced to explain the theoretic parts.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"224 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130272356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Blow up of nonautonomous fractional reaction-diffusion systems 非自治分数反应扩散系统的爆破
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2020-10-01
Aroldo Pérez
{"title":"Blow up of nonautonomous fractional reaction-diffusion systems","authors":"Aroldo Pérez","doi":"10.7153/fdc-2020-10-01","DOIUrl":"https://doi.org/10.7153/fdc-2020-10-01","url":null,"abstract":". We provide a suf fi cient condition for fi nite time blow up of the positive mild solution to the nonautonomous Cauchy problem of a reaction-diffusion system with distinct fractional diffusions. The proof is based on the reduction to an ordinary differential system by means of a comparison between the transition densities of the semigroups generated by the different fractional Laplacians. Moreover, we prove that this condition is also a suf fi cient condition for the blow up of a related nonautonomous fractional diffusion-convection-reaction system.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129992642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Controllability and observability of time-invariant linear nabla fractional systems 定常线性nabla分数系统的可控性和可观测性
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2020-10-02
F. Atici, Tilekbek Zhoroev
{"title":"Controllability and observability of time-invariant linear nabla fractional systems","authors":"F. Atici, Tilekbek Zhoroev","doi":"10.7153/fdc-2020-10-02","DOIUrl":"https://doi.org/10.7153/fdc-2020-10-02","url":null,"abstract":". In this paper, we study linear time-invariant nabla fractional discrete control systems. The nabla fractional difference operator is considered in the sense of Riemann-Liouville def-inition of the fractional derivative. We fi rst give necessary and suf fi cient rank conditions for controllability of the discrete fractional system via Gramian and controllability matrices. We then obtain rank conditions for observability of the discrete fractional system. We illustrate main results with some numerical examples. We close the paper by stating that the rank conditions for the time-invariant linear dynamic system on time scales, fractional system in continuous time, and fractional system in discrete time coincide.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134182716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some results on mixed fractional integrodifferential equation in matrix MB-space 矩阵mb空间中混合分数阶积分微分方程的一些结果
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2023-13-05
V. V. Kharat, A. R. Reshimkar
{"title":"Some results on mixed fractional integrodifferential equation in matrix MB-space","authors":"V. V. Kharat, A. R. Reshimkar","doi":"10.7153/fdc-2023-13-05","DOIUrl":"https://doi.org/10.7153/fdc-2023-13-05","url":null,"abstract":"","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122963019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sufficient conditions for the exponential stability of nonlinear fractionally perturbed ODEs with multiple time delays 多时滞非线性分数摄动ode指数稳定性的充分条件
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2019-09-17
M. Medved', Eva Brestovanská
{"title":"Sufficient conditions for the exponential stability of nonlinear fractionally perturbed ODEs with multiple time delays","authors":"M. Medved', Eva Brestovanská","doi":"10.7153/fdc-2019-09-17","DOIUrl":"https://doi.org/10.7153/fdc-2019-09-17","url":null,"abstract":"In this paper we prove some results on the exponential stability of the trivial solution of a system of fractional differential equations with multiple delays and tempered RiemannLouville fractional integrals on its right-hand side.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128760678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Hilfer and Hadamard coupled Volterra fractional integro-differential systems with random effects Hilfer和Hadamard耦合具有随机效应的Volterra分数阶积分微分系统
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/FDC-2019-09-01
S. Abbas, R. Agarwal, M. Benchohra, Boualem Attou Slimani
{"title":"Hilfer and Hadamard coupled Volterra fractional integro-differential systems with random effects","authors":"S. Abbas, R. Agarwal, M. Benchohra, Boualem Attou Slimani","doi":"10.7153/FDC-2019-09-01","DOIUrl":"https://doi.org/10.7153/FDC-2019-09-01","url":null,"abstract":". This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer-Hadamard random fractional integro-differential equations. The main tool used to carry out our results is Itoh’s random fi xed point theorem.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125441918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions 非局部多点边界条件下的分数阶积分-微分包体
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/FDC-2019-09-10
A. Cernea
{"title":"On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions","authors":"A. Cernea","doi":"10.7153/FDC-2019-09-10","DOIUrl":"https://doi.org/10.7153/FDC-2019-09-10","url":null,"abstract":". Existence of solutions for two classes of fractional integro-differential inclusions with nonlocal multi-point boundary conditions is investigated in the case when the values of the set-valued map are not convex.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"164 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132844685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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