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Axioms 2018, 7(4), 89; https://doi.org/10.3390/axioms7040089

A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Escuela de Matemáticas, Universidad Nacional de Colombia, Carrera 65 # 59 A-110, Medellín 050034, Colombia
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 16 September 2018 / Revised: 13 November 2018 / Accepted: 20 November 2018 / Published: 23 November 2018
(This article belongs to the Special Issue Applications of Differential Equations and Dynamical Systems)
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Abstract

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included. View Full-Text
Keywords: inverse problem; mollification; fractional derivatives inverse problem; mollification; fractional derivatives
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Echeverry, M.D.; Mejía, C.E. A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem. Axioms 2018, 7, 89.

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