Unique determination of the initial values of the time-fractional diffusion-wave equation by lateral Cauchy data

Year 2025, Volume: 54 Issue: 5, 1859 - 1871, 29.10.2025

Xuyan Jiang , Zhiyuan Li

https://doi.org/10.15672/hujms.1525278

Abstract

This paper focuses on the determination of initial values in fractional wave equations. As is known, there are two initial conditions in fractional wave equations, and we aim to reconstruct these two unknown quantities through the minimum possible lateral Cauchy data. We construct the Liouville theorem on complex plane with the negative real axis removed, which helps us to prove the uniqueness of the inverse problem under consideration. In the final section of this paper, we propose an algorithm that utilizes lateral Cauchy data to recover the two initial values.

Keywords

lateral cauchy data , time fractional , initial values

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