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Fractional Differential Equations最新文献

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Inverse problems of determining parameters of the fractional partial differential equations 分数阶偏微分方程参数确定的反问题
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-019
Zhi-yuan Li, Yikan Liu, Masahiro Yamamoto
{"title":"Inverse problems of determining parameters of the fractional partial differential equations","authors":"Zhi-yuan Li, Yikan Liu, Masahiro Yamamoto","doi":"10.1515/9783110571660-019","DOIUrl":"https://doi.org/10.1515/9783110571660-019","url":null,"abstract":"When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be directly measured, which requires one to discuss inverse problems of identifying these physical quantities from some indirectly observed information of solutions. Inverse problems in determining these unknown parameters of the model are not only theoretically interesting, but also necessary for finding solutions to initial-boundary value problems and studying properties of solutions. This chapter surveys works on such inverse problems for fractional diffusion equations.","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121436050","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: 50
Abstract linear fractional evolution equations 抽象的线性分数进化方程
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-021
C. Lizama
{"title":"Abstract linear fractional evolution equations","authors":"C. Lizama","doi":"10.1515/9783110571660-021","DOIUrl":"https://doi.org/10.1515/9783110571660-021","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124496332","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: 23
Equations with general fractional time derivatives–Cauchy problem 具有一般分数阶时间导数的方程-柯西问题
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-011
A. Kochubei
{"title":"Equations with general fractional time derivatives–Cauchy problem","authors":"A. Kochubei","doi":"10.1515/9783110571660-011","DOIUrl":"https://doi.org/10.1515/9783110571660-011","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130201378","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: 22
Wave equation involving fractional derivatives of real and complex fractional order 涉及实阶和复阶分数阶导数的波动方程
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-015
T. Atanacković, S. Konjik, S. Pilipovic
{"title":"Wave equation involving fractional derivatives of real and complex fractional order","authors":"T. Atanacković, S. Konjik, S. Pilipovic","doi":"10.1515/9783110571660-015","DOIUrl":"https://doi.org/10.1515/9783110571660-015","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115594732","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
Frontmatter
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-fm
{"title":"Frontmatter","authors":"","doi":"10.1515/9783110571660-fm","DOIUrl":"https://doi.org/10.1515/9783110571660-fm","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114307861","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
Problems of Sturm–Liouville type for differential equations with fractional derivatives 分数阶微分方程的Sturm-Liouville型问题
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-002
T. Aleroev, H. Aleroeva
{"title":"Problems of Sturm–Liouville type for differential equations with fractional derivatives","authors":"T. Aleroev, H. Aleroeva","doi":"10.1515/9783110571660-002","DOIUrl":"https://doi.org/10.1515/9783110571660-002","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129639507","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: 14
Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps 映射与幂律记忆:直接介绍和欧拉数，分数映射，和分数差分映射
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-003
M. Edelman
{"title":"Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps","authors":"M. Edelman","doi":"10.1515/9783110571660-003","DOIUrl":"https://doi.org/10.1515/9783110571660-003","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128077352","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: 18
Operational method for fractional ordinary differential equations 分数阶常微分方程的运算方法
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-005
Yuri Luchko
{"title":"Operational method for fractional ordinary differential equations","authors":"Yuri Luchko","doi":"10.1515/9783110571660-005","DOIUrl":"https://doi.org/10.1515/9783110571660-005","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116583607","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
Inverse problems of determining sources of the fractional partial differential equations 确定分数阶偏微分方程源的反问题
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-018
Yikan Liu, Zhi-yuan Li, Masahiro Yamamoto
{"title":"Inverse problems of determining sources of the fractional partial differential equations","authors":"Yikan Liu, Zhi-yuan Li, Masahiro Yamamoto","doi":"10.1515/9783110571660-018","DOIUrl":"https://doi.org/10.1515/9783110571660-018","url":null,"abstract":"In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order α ∈ (0, 1). Our survey covers the following types of inverse problems: • determination of time-dependent functions in interior source terms • determination of space-dependent functions in interior source terms • determination of time-dependent functions appearing in boundary conditions","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127597795","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: 49
Symmetries, conservation laws and group invariant solutions of fractional PDEs 分数阶偏微分方程的对称性、守恒律和群不变解
Fractional Differential Equations Pub Date : 2019-02-18 DOI: 10.1515/9783110571660-016
R. Gazizov, A. A. Kasatkin, S. Lukashchuk
{"title":"Symmetries, conservation laws and group invariant solutions of fractional PDEs","authors":"R. Gazizov, A. A. Kasatkin, S. Lukashchuk","doi":"10.1515/9783110571660-016","DOIUrl":"https://doi.org/10.1515/9783110571660-016","url":null,"abstract":"","PeriodicalId":313977,"journal":{"name":"Fractional Differential Equations","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123119539","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: 12
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