Estimation and numerical approximation for a type of time fractional delay diffusion equation

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Abstract

An improved single-component Metropolis–Hastings (ISC–MH) algorithm for estimating a kind of time fractional delay diffusion equation (FDDE) is provided. We introduce the symmetric proposal distribution for generating the candidate point of each parameter to obtain the ISC–MH algorithm. To estimate the unknown parameter of the FDDE, firstly, we construct the compact difference scheme to numerically discretize the FDDE. Then the ISC–MH algorithm is used to estimate the fractional order, the diffusion coefficient, and the time delay in the system of the FDDE simultaneously. Finally, some simulation tests of two examples are provided to validate the performance of the algorithms.

Keywords

fractional order / time delay / the compact difference scheme / improved single-component Metropolis–Hastings algorithm

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