On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces
Joint Authors
Li, Cheng-Gang
Kostić, Marko
Li, Miao
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-41, 41 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-11
Country of Publication
Egypt
No. of Pages
41
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Kostić, Marko& Li, Cheng-Gang& Li, Miao. 2012. On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-41.
https://search.emarefa.net/detail/BIM-448188
Modern Language Association (MLA)
Kostić, Marko…[et al.]. On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces. Abstract and Applied Analysis No. 2012 (2012), pp.1-41.
https://search.emarefa.net/detail/BIM-448188
American Medical Association (AMA)
Kostić, Marko& Li, Cheng-Gang& Li, Miao. On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-41.
https://search.emarefa.net/detail/BIM-448188
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-448188