dc.contributor.author Lizama, C. dc.contributor.author Murillo-Arcila, M. dc.date.accessioned 2017-06-08T15:06:01Z dc.date.available 2017-06-08T15:06:01Z dc.date.issued 2017-05-01 dc.identifier.issn 0022-0396 dc.identifier.uri http://hdl.handle.net/20.500.11824/682 dc.description.abstract In 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 en_US $$\Delta^{\alpha}u(n,x) = Au(n ,x) + \sum_{j=1}^k \beta_j u(n-\tau_j,x) +f(n,u(n,x)),\,\,\, n \in \mathbb{Z}, x \in \Omega \subset \mathbb{R}^N, \beta_j\in\mathbb{R}\hspace{0.1cm}\mbox{and}\hspace{0.1cm} \tau_j \in \mathbb{Z},$$ 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. dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Maximal $l_p$-regularity en_US dc.subject Shifted equations en_US dc.subject Discrete time en_US dc.subject Grünwald–Letnikov derivative en_US dc.title Maximal regularity in $l_p$ spaces for discrete time fractional shifted equations en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1016/j.jde.2017.04.035 dc.relation.publisherversion http://www.sciencedirect.com/science/article/pii/S0022039617302462 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Journal of Differential Equations en_US
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