Identifying initial value problem for time‐fractional diffusion equation with Caputo‐like counterpart hyper‐Bessel operator: Optimal error bound analysis and regularization method

Abstract

In this paper, we consider the inverse problem for identifying the initial value problem for time-fractional diffusion equation with hyper-Bessel operator. Firstly, we show that this problem is ill-posed and analyze the optimal error bound. Next, we use the fractional Landweber iterative regularization method to solve this problem and give the error estimates between the regularization solution and the exact solution under the a priori regularization parameter choice rule and a posteriori regularization parameter choice rule. Finally, we use numerical examples to verify the effectiveness of this method. KEYWORDS Caputo-like counterpart hyper-Bessel operator, fractional Landweber regularization, ill-posed problem, initial value problem, time-fractional diffusion equation MSC CLASSIFICATION 35R25; 47A52; 35R30How to cite this article: Yang F, Sun Q-X, Li X-X. Identifying initial value problem for time-fractional diffusion equation with Caputo-like counterpart hyper-Bessel operator: Optimal error bound analysis and regularization method.