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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/131652 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |