Three regularization methods for identifying the initial value of homogeneous anomalous secondary diffusion equation

Abstract

In this paper, the inverse problem of initial value identification for homogeneous anomalous diffusion equation with Riemann‐Liouville fractional derivative in time is studied. We prove that this kind of problem is ill‐posed. We analyze the optimal error bound of the problem under the source condition and apply the quasi‐boundary regularization method, fractional Landweber iterative regularization method, and Landweber iterative regularization method to solve this inverse problem. Based on the results of conditional stability, the error estimates between the exact solution and the regular solution are given under the priori and posteriori regularization parameter selection rules. Finally, three examples are given to illustrate the effectiveness and feasibility of these methods.