Abstract

An inversion problem of estimating parameters for a one-dimensional time fractional thermal wave equation with fractional heat flux conditions and Caputo fractional derivatives is investigated. To begin with, the analytical solution of the direct problem is obtained. Then, based on the parameter sensitivity analysis, the least-squares method is used to estimate both the fractional order α and the relaxation time τ simultaneously. Finally, two different heat flux distributions are given as different boundary conditions to perform the simulation experiments, respectively. By analyzing the degree of fitting curves, results show that the least-squares method performs well in parameter estimation for this fractional thermal wave equation. This study provides an effective method of estimating the parameters of fractional thermal wave equations.

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