On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces
This paper is devoted to the study of abstract time-fractional equations of the following form: Dtαnu(t)+∑i=1n−1AiDtαiu(t)=ADtαu(t)+f(t), t>0, u(k)(0)=uk, k=0,...,⌈αn⌉−1, where n∈ℕ∖{1}, A and A1,...,An−1 are closed linear operators on a sequentially complete locally convex space E,0≤α1<⋯<αn...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/131652 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551591450771456 |
|---|---|
| author | Marko Kostić Cheng-Gang Li Miao Li |
| author_facet | Marko Kostić Cheng-Gang Li Miao Li |
| author_sort | Marko Kostić |
| collection | DOAJ |
| description | This paper is devoted to the study of abstract time-fractional equations of the following form:
Dtαnu(t)+∑i=1n−1AiDtαiu(t)=ADtαu(t)+f(t), t>0, u(k)(0)=uk, k=0,...,⌈αn⌉−1, where n∈ℕ∖{1}, A and A1,...,An−1 are closed linear operators on a sequentially complete locally convex space E,0≤α1<⋯<αn, 0≤α<αn, f(t) is an E-valued function, and Dtα denotes the Caputo fractional derivative of order α (Bazhlekova (2001)). We introduce and systematically analyze various classes of k-regularized (C1,C2)-existence and uniqueness (propagation) families, continuing in such a way the researches raised in (de Laubenfels (1999, 1991), Kostić (Preprint), and Xiao and Liang (2003, 2002). The obtained results are illustrated with several examples. |
| format | Article |
| id | doaj-art-20edbfdff3bd420ca584e8bb63b138c8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-20edbfdff3bd420ca584e8bb63b138c82025-02-03T06:00:59ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/131652131652On a Class of Abstract Time-Fractional Equations on Locally Convex SpacesMarko Kostić0Cheng-Gang Li1Miao Li2Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, SerbiaDepartment of Mathematics, Sichuan University, Chengdu 610064, ChinaDepartment of Mathematics, Sichuan University, Chengdu 610064, ChinaThis paper is devoted to the study of abstract time-fractional equations of the following form: Dtαnu(t)+∑i=1n−1AiDtαiu(t)=ADtαu(t)+f(t), t>0, u(k)(0)=uk, k=0,...,⌈αn⌉−1, where n∈ℕ∖{1}, A and A1,...,An−1 are closed linear operators on a sequentially complete locally convex space E,0≤α1<⋯<αn, 0≤α<αn, f(t) is an E-valued function, and Dtα denotes the Caputo fractional derivative of order α (Bazhlekova (2001)). We introduce and systematically analyze various classes of k-regularized (C1,C2)-existence and uniqueness (propagation) families, continuing in such a way the researches raised in (de Laubenfels (1999, 1991), Kostić (Preprint), and Xiao and Liang (2003, 2002). The obtained results are illustrated with several examples.http://dx.doi.org/10.1155/2012/131652 |
| spellingShingle | Marko Kostić Cheng-Gang Li Miao Li On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces Abstract and Applied Analysis |
| title | On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces |
| title_full | On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces |
| title_fullStr | On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces |
| title_full_unstemmed | On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces |
| title_short | On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces |
| title_sort | on a class of abstract time fractional equations on locally convex spaces |
| url | http://dx.doi.org/10.1155/2012/131652 |
| work_keys_str_mv | AT markokostic onaclassofabstracttimefractionalequationsonlocallyconvexspaces AT chenggangli onaclassofabstracttimefractionalequationsonlocallyconvexspaces AT miaoli onaclassofabstracttimefractionalequationsonlocallyconvexspaces |