Parameter and differentiation order estimation for a two dimensional fractional partial differential equation

Abeer Aldoghaither, Taous-Meriem Laleg-Kirati

Research output: Contribution to journalArticlepeer-review

Abstract

This paper deals with the estimation of coefficients and differentiation orders for two-dimensional fractional partial differential equations. Recently, a hybrid method based on modulating functions has been proposed by the authors to estimate the coefficients and a differentiation order for a one dimensional fractional advection dispersion equation in Aldoghaither et al. (2015). We propose to extend this method to the two-dimensional case. First, the coefficients are estimated using a modulating functions method, where the problem is transferred into solving a system of algebraic equations. Then, the modulating functions method combined with a Newton algorithm is proposed to estimate the coefficients and the differentiation orders simultaneously. Numerical example is presented with noisy measurements to show the effectiveness and the robustness of the method.
Original languageEnglish (US)
Pages (from-to)112570
JournalJournal of Computational and Applied Mathematics
Volume369
DOIs
StatePublished - Nov 6 2019

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