关键词: 热波方程, 分数阶导数, 渐近解

Abstract: A class of nonlinear generalized thermal wave equation was considered .Firstly， the solution to reduced thermal wave equation was obtained.Next， the arbitrary order asymptopic solutions to generalized nonlinear disturbed thermal wave equation initial-boundary value problem were constructed by using the method of functional analysis homotopic mapping.An example was given and the accuracy of its asymptopic solution was obtained.Finally， the physical sense of the solution was briefly stated. The approximate analysis solution makes up for the simple numerical simulation solution deficiency.

Key words: thermal wave equation, fractional order derivative, asymptotic solution