Regularization of a backward problem for composite fractional relaxation equations

Abstract

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.