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dc.contributor.authorMejía Salazar, Carlos E.-
dc.date.accessioned2021-12-09T23:38:28Z-
dc.date.available2021-12-09T23:38:28Z-
dc.date.issued2019-09-25-
dc.identifier.urihttps://repositorio.accefyn.org.co/handle/001/1163-
dc.description.abstractEste artículo trata sobre operadores de molificación discreta y sobre derivadas fraccionarias. Los operadores de molificación se definen a partir de convoluciones con núcleos gaussianos truncados, tanto en una como en dos dimensiones. Iniciamos con una descripción de sus orígenes y de sus principales propiedades y después consideramos en detalle dos aplicaciones que indican lo útiles que son estos operadores. Las aplicaciones se basan en ecuaciones diferenciales parciales difusivas con derivadas temporales fraccionarias. Estas derivadas merecen el calificativo de ilustres como se verá más adelante. La primera aplicación consiste en la solución estable de un problema inverso de advección-dispersión, con derivada temporal fraccionaria, en el que la concentración es desconocida en la frontera de un dominio unidimensional semi-infinito. La segunda aplicación es la solución estable de un problema inverso bidimensional de identificación de un término fuente en una ecuación de difusión con derivada temporal fraccionaria. En cada caso se incluye la descripción del problema, la implementación de la molificación, el método de solución y algunos experimentos numéricos. Para el problema en dos dimensiones incluímos resultados recientemente enviados para publicación.spa
dc.description.abstractThis paper deals with discrete mollification operators and fractional derivatives. The mollification operators are based on convolutions with truncated Gaussian kernels in one and two dimensions. We begin with a description of their origin and main properties and then we consider two applications that show the usefulness of these operators. Both applications are based on time-fractional diffusion equations. Fractional derivatives deserve to be called illustrious, as we will see later. The first application consists of the stable solution of an inverse problem for a time fractional advection-dispersion equation. The problem consists of the identification of the boundary concentration in a one-dimensional semi-infinite setting. The second application is the stable solution of a problem of source term identification in a bidimensional time-fractional diffusion equation. In each case, we include a description of the problem, the mollification implementation, the method of solution, and some numerical experiments. For the two dimensions problem we include results that were recently published.eng
dc.format.mimetypeapplication/pdfspa
dc.language.isospaspa
dc.publisherAcademia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 Internationalspa
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/spa
dc.sourceRevista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.titleUna convolución muy útil y unas derivadas ilustresspa
dc.typeArtículo de revistaspa
dcterms.audienceEstudiantes, Profesores, Comunidad científica colombianaspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.type.driverinfo:eu-repo/semantics/articlespa
dc.type.versioninfo:eu-repo/semantics/publishedVersionspa
dc.rights.creativecommonsAtribución-NoComercial 4.0 Internacional (CC BY-NC 4.0)spa
dc.identifier.doihttps://doi.org/10.18257/raccefyn.767-
dc.subject.proposalConvoluciónspa
dc.subject.proposalConvolutioneng
dc.subject.proposalDerivadas fraccionariasspa
dc.subject.proposalFractional derivativeseng
dc.subject.proposalMolificación discretaspa
dc.subject.proposalDiscrete mollificationeng
dc.subject.proposalProblemas inversosspa
dc.subject.proposalInverse problemseng
dc.type.coarhttp://purl.org/coar/resource_type/c_6501spa
dc.relation.ispartofjournalRevista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.relation.citationvolume43spa
dc.relation.citationstartpage563spa
dc.relation.citationendpage571spa
dc.publisher.placeBogotá, Colombiaspa
dc.contributor.corporatenameAcademia Colombiana de Ciencias Exactas, Físicas y Naturalesspa
dc.relation.citationissue168spa
dc.type.contentDataPaperspa
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