On the Inverse Problem of the Fractional Heat-Like Partial Differential Equations: Determination of the Source Function

摘要

The study in this paper mainly concerns the inverse problem of determining an unknown source function in the linear fractional differential equation with variable coefficient using Adomian decomposition method (ADM). We apply ADM to determine the continuous right hand side functionsfxandftin the heat-like diffusion equationsDtαux,t=hxuxxx,t+fxandDtαux,t=hxuxxx,t+ft, respectively. The results reveal that ADM is very effective and simple for the inverse problem of determining the source function.