¹University of Cincinnati, Ohio, USA. Email: diego@dmurio.csm.uc.edu
²University of Cincinnati, Ohio, USA. Email: cemejia@unal.edu.co

We introduce a regularization technique for the approximate reconstruction of spatial and time varying source terms using the observed solutions of the forward time fractional diffusion problem on a discrete set of points. The numerical method is based on computation of the derivatives of adaptive filtered versions of the noisy data by discrete mollification.

Key words: Ill-Posed Problems, heat source identification, Caputofractional derivatives, time fractional diffusion equation, mollification techniques.

Presentamos una técnica de regularización para la reconstrucción numérica de términos fuente dependientes de espacio y tiempo a partir de aproximaciones de la solución del problema directo en un conjunto discreto de puntos. El método se basa en el cálculo de derivadas de versiones de los datos aproximados que se obtienen con el filtro adaptativo denominado molificación discreta.

Palabras clave: Problemas mal condicionados, identificación de una fuente de calor, derivadas fraccionales de Caputo, ecuación de difusión con derivadafraccional en la dirección del tiempo, técnicas de molificación.

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