Two Regularization Methods for Identifying the Initial Value of Time-Fractional Telegraph Equation

Abstract In this article, an inverse problem for identifying the initial value of time-fractional telegraph equation is addressed. This is a typical ill-posed problem, meaning the solution does not depend continuously on the data. Besides, we give the conditional stability result based on an a priori bound condition. We utilize the modified quasi-boundary regularization method and the Landweber iterative regularization method to obtain the corresponding approximate solutions, respectively. The convergent error estimates under the a priori regularization parameter selection rule and the a posteriori regularization parameter selection rule are given. Some numerical experiments testify the effectiveness and precision of the proposed methods.