4.6 Article

Regularization of a backward problem for composite fractional relaxation equations

Journal

MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 46, Issue 1, Pages 180-196

Publisher

WILEY
DOI: 10.1002/mma.8503

Keywords

backward problem; composite relaxation equations; fractional derivative; fractional Landweber regularization method

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This article considers the backward problem for composite fractional relaxation equations using Caputo's fractional derivative. The representation of solutions is established based on a spectral problem, and the maximal regularity for the corresponding initial value problem is shown. Due to the mildly ill-posedness of the current backward problem, the fractional Landweber regularization method is applied to discuss convergence analysis and error estimates.
A backward problem for composite fractional relaxation equations is considered with Caputo's fractional derivative, which covers as particular case of Basset problem that concerns the unsteady motion of a particle accelerating in a viscous fluid in fluid dynamics. Based on a spectral problem, the representation of solutions is established. Next, we show the maximal regularity for the corresponding initial value problem. Due to the mildly ill-posedness of current backward problem, the fractional Landweber regularization method will be applied to discuss convergence analysis and error estimates.

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