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- Title
On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces.
- Authors
Kostić, Marko; Li, Cheng-Gang; Li, Miao
- Abstract
This paper is devoted to the study of abstract time-fractional equations of the following form: ..., where n ε N \ {1}, A and A1, ...,An-1 are closed linear operators on a sequentially complete locally convex space E, 0 = a1 < · · · < an, 0 = a < an, f(t) is an E-valued function, and Dat denotes the Caputo fractional derivative of order a (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.
- Subjects
CONVEX functions; LINEAR operators; EXISTENCE theorems; CAPUTO fractional derivatives; MATHEMATICAL sequences; OPERATOR theory
- Publication
Abstract & Applied Analysis, 2012, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2012/131652