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2012 On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces
Marko Kostić, Cheng-Gang Li, Miao Li
Abstr. Appl. Anal. 2012(SI01): 1-41 (2012). DOI: 10.1155/2012/131652

Abstract

This paper is devoted to the study of abstract time-fractional equations of the following form: D t α n u ( t ) + i = 1 n 1 A i D t α i u ( t ) = A D t α u ( t ) + f ( t ) , t > 0 , u ( k ) ( 0 ) = u k , k = 0 , ... , α n 1 , where n { 1 } , A and A 1 , ... , A n 1 are closed linear operators on a sequentially complete locally convex space E , 0 α 1 < < α n , 0 α < α n , f ( t ) is an E -valued function, and D t α denotes the Caputo fractional derivative of order α (Bazhlekova (2001)). We introduce and systematically analyze various classes of k -regularized ( C 1 , C 2 )-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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Marko Kostić. Cheng-Gang Li. Miao Li. "On a Class of Abstract Time-Fractional Equations on Locally Convex Spaces." Abstr. Appl. Anal. 2012 (SI01) 1 - 41, 2012. https://doi.org/10.1155/2012/131652

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1311.47058
MathSciNet: MR2994949
Digital Object Identifier: 10.1155/2012/131652

Rights: Copyright © 2012 Hindawi

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