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dc.contributor.authorLizama, C.
dc.contributor.authorMurillo-Arcila, M.
dc.date.accessioned2017-06-08T15:06:01Z
dc.date.available2017-06-08T15:06:01Z
dc.date.issued2017-05-01
dc.identifier.issn0022-0396
dc.identifier.urihttp://hdl.handle.net/20.500.11824/682
dc.description.abstractIn this paper, we are presenting a new method based on operator-valued Fourier multipliers to \- characterize the existence and uniqueness of $\ell_p$-solutions for discrete time fractional models in the form $$ \Delta^{\alpha}u(n,x) = Au(n ,x) + \sum_{j=1}^k \beta_j u(n-\tau_j,x) +f(n,u(n,x)),\,\,\, n \in \mathbb{Z}, x \in \Omega \subset \mathbb{R}^N, \beta_j\in\mathbb{R}\hspace{0.1cm}\mbox{and}\hspace{0.1cm} \tau_j \in \mathbb{Z}, $$ where $A$ is a closed linear operator defined on a Banach space $X$ and $\Delta^{\alpha}$ denotes the Gr\"unwald-Letnikov fractional derivative of order $\alpha>0.$ If $X$ is a $UMD$ space, we provide this characterization only in terms of the $R$-boundedness of the operator-valued symbol associated to the abstract model. To illustrate our results, we derive new qualitative properties of nonlinear difference equations with shiftings, including fractional versions of the logistic and Nagumo equations.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectMaximal $l_p$-regularityen_US
dc.subjectShifted equationsen_US
dc.subjectDiscrete timeen_US
dc.subjectGrünwald–Letnikov derivativeen_US
dc.titleMaximal regularity in $l_p$ spaces for discrete time fractional shifted equationsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1016/j.jde.2017.04.035
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0022039617302462en_US
dc.relation.projectIDES/1PE/SEV-2013-0323en_US
dc.relation.projectIDEUS/BERC/BERC.2014-2017en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleJournal of Differential Equationsen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
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