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Abstract
Este 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.
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