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

Chaoqin Yi; Peiyan Li; Wei Gu; Chaoqin Yi; Peiyan Li; Wei Gu

doi:10.3934/era.2026247

Electronic Research Archive

2026, Volume 34, Issue 8: 5525-5545. doi: 10.3934/era.2026247

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

1.
Department of General Education, Shanghai Urban Construction Vocational College, Shanghai 201415, China
2.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
3.
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received: 26 March 2026 Revised: 09 June 2026 Accepted: 16 June 2026 Published: 30 June 2026

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.
- fractional order,
- time delay,
- the compact difference scheme,
- improved single-component Metropolis–Hastings algorithm
Citation: Chaoqin Yi, Peiyan Li, Wei Gu. Estimation and numerical approximation for a type of time fractional delay diffusion equation[J]. Electronic Research Archive, 2026, 34(8): 5525-5545. doi: 10.3934/era.2026247

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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.

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