Almost automorphic mild solutions to fractional partial difference-differential equations. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Abadias, Luciano; Lizama, Carlos
• Is Part Of: Applicable analysis. Volume 95:Issue 6(2016)
• Page Start: 1347
• Page End: 1369
• Publication Date: 2016-06-02
• Subjects: Weyl-like fractional difference -- almost automorphic sequence -- -semigroups -- fractional difference equations -- mild solution; 35R11 -- 34A08 -- 43A60 -- 47D06; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1064521
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We study existence and uniqueness of almost automorphic solutions for nonlinear partial difference-differential equations modeled in abstract form as (*) for where is the generator of a -semigroup defined on a Banach space, denote fractional difference in Weyl-like sense and satisfies Lipchitz conditions of global and local type. We introduce the notion of -resolvent sequence and we prove that a mild solution of corresponds to a fixed point of We show that such mild solution is strong in case of the forcing term belongs to an appropriate weighted Lebesgue space of sequences. Application to a model of population of cells is given.