A posteriori error estimates of spectral method for the fractional optimal control problems with non-homogeneous initial conditions

In this paper we consider an optimal control problem governed by a space-time fractional diffusion equation with non-homogeneous initial conditions. A spectral method is proposed to discretize the problem in both time and space directions. The contribution of the paper is threefold: (1) A discussion...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 11; pp. 12028 - 12050
Main Authors Ye, Xingyang, Xu, Chuanju
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
a posteriori error
fractional optimal control problem
initial conditions
spectral method
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021697

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Summary:In this paper we consider an optimal control problem governed by a space-time fractional diffusion equation with non-homogeneous initial conditions. A spectral method is proposed to discretize the problem in both time and space directions. The contribution of the paper is threefold: (1) A discussion and better understanding of the initial conditions for fractional differential equations with Riemann-Liouville and Caputo derivatives are presented. (2) A posteriori error estimates are obtained for both the state and the control approximations. (3) Numerical experiments are performed to verify that the obtained a posteriori error estimates are reliable.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021697