On a Backward Problem for the Rayleigh–Stokes Equation with a Fractional Derivative

Abstract

The Rayleigh–Stokes equation with a fractional derivative is widely used in many fields. In this paper, we consider the inverse initial value problem of the Rayleigh–Stokes equation. Since the problem is ill-posed, we adopt the Tikhonov regularization method to solve this problem. In addition, this paper not only analyzes the ill-posedness of the problem but also gives the conditional stability estimate. Finally, the convergence estimates are proved under two regularization parameter selection rules.

Keywords

• Rayleigh–Stokes equation with a fractional derivative
• backward problem
• Tikhonov regularization method
• convergence estimate