Regularization of a backward problem for composite fractional relaxation equations

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.

Automated summary

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.