On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces

Marko Kostić, Cheng-Gang Li and Miao Li

Abstract and Applied Analysis, 2012, vol. 2012, 1-41

Abstract:

This paper is devoted to the study of abstract time-fractional equations of the following form: , , , , where , and are closed linear operators on a sequentially complete locally convex space , , is an -valued function, and denotes the Caputo fractional derivative of order (Bazhlekova (2001)). We introduce and systematically analyze various classes of -regularized ( )-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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:131652

DOI: 10.1155/2012/131652

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