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Well posedness for semidiscrete fractional Cauchy problems with finite delay
dc.contributor.author | Lizama, Carlos | |
dc.contributor.author | murillo arcila, marina | |
dc.date.accessioned | 2017-11-07T10:28:53Z | |
dc.date.available | 2017-11-07T10:28:53Z | |
dc.date.issued | 2017-08 | |
dc.identifier.citation | LIZAMA, Carlos; MURILLO-ARCILA, Marina. Well posedness for semidiscrete fractional Cauchy problems with finite delay. Journal of Computational and Applied Mathematics, 2017. | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/169883 | |
dc.description.abstract | We address the study of well posedness on Lebesgue spaces of sequences for the following fractional semidiscrete model with finite delay ∆ α u ( n ) = Tu ( n ) + β u ( n − τ ) + f ( n ) , n ∈ N , 0 < α ≤ 1 , β ∈ R , τ ∈ N 0 , (0.1) where is a bounded linear operator defined on a Banach space (typically a space of functions like ) and corresponds to the time discretization of the continuous Riemann–Liouville fractional derivative by means of the Poisson distribution. We characterize the existence and uniqueness of solutions in vector-valued Lebesgue spaces of sequences of the model (0.1) in terms of boundedness of the operator-valued symbol (( z − 1) α z 1 − α I − β z − τ − T ) − 1 , | z |= 1 , z ̸= 1 , whenever and satisfies a geometrical condition. For this purpose, we use methods from operator-valued Fourier multipliers and resolvent operator families associated to the homogeneous problem. We apply this result to show a practical and computational criterion in the context of Hilbert spaces. | ca_CA |
dc.format.extent | 14 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.rights | © 2017 Elsevier B.V. All rights reserved. | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Fractional differences | ca_CA |
dc.subject | Delay equations | ca_CA |
dc.subject | Well-posedness | ca_CA |
dc.subject | Maximal regularity | ca_CA |
dc.subject | Operator-valued Fourier multiplier | ca_CA |
dc.title | Well posedness for semidiscrete fractional Cauchy problems with finite delay | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.cam.2017.07.027 | |
dc.relation.projectID | CONICYT under FONDECYT (Grant Number 1140258 and CONICYT-PIA-Anillo ACT1416) ; Basque Government (BERC 2014–2017 program) ; Spanish Ministry of Economy and Competitiveness MINECO (MTM2016-75963-P): BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and 644202 GEAGAM, H2020-MSCA-RISE-2014. | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | http://www.sciencedirect.com/science/article/pii/S0377042717303783 | ca_CA |
dc.type.version | info:eu-repo/semantics/submittedVersion | ca_CA |
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