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https://open.uns.ac.rs/handle/123456789/14496
Title: | On a class of abstract time-fractional equations on locally convex spaces | Authors: | Kostić, Marko Li C. Li M. |
Issue Date: | 27-Dec-2012 | Journal: | Abstract and Applied Analysis | Abstract: | This paper is devoted to the study of abstract time-fractional equations of the following form: Dtαn u(t) + =;i=1n-1 AiDtα;i u (t) = ADtαu(t) + f(t), t > 0, u(k)(0) = uk, k = 0,⋯, ⌈αn⌉ - 1, where n ε 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. Copyright © 2012 Marko Kostić et al. | URI: | https://open.uns.ac.rs/handle/123456789/14496 | ISSN: | 10853375 | DOI: | 10.1155/2012/131652 |
Appears in Collections: | FTN Publikacije/Publications |
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