Well posedness for semidiscrete fractional Cauchy problems with finite delay
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Title
Well posedness for semidiscrete fractional Cauchy problems with finite delayDate
2017-08Publisher
ElsevierBibliographic citation
LIZAMA, Carlos; MURILLO-ARCILA, Marina. Well posedness for semidiscrete fractional Cauchy problems with finite delay. Journal of Computational and Applied Mathematics, 2017.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0377042717303783Version
info:eu-repo/semantics/submittedVersionSubject
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 ... [+]
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. [-]
Investigation project
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.Rights
© 2017 Elsevier B.V. All rights reserved.
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info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
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