Notes on “The Cattaneo-type time fractional heat conduction equation for laser heating” [Comput. Math. Appl. 66 (2013) 824–831]

In this paper, Eq. (6) in Qi et al. (2013) is corrected by pointing out the missing time delayed fractional derivative item of I1δ⋅g(x)τpDtpf(t)/k. The time fractional heat conduction model is used as the constitutive heat diffusion model and the corresponding fractional heat conduction equation with a volumetric heat source is built. Subjected to the same initial and boundary conditions as those in Qi et al. (2013), the analytical solution is presented. Furthermore, the dimensionless temperature variations and distributions are shown graphically with various values of fractional order and delayed time parameters. Compared with the previous curves in Qi et al. (2013), the obtained temperature variation and distribution are different and even opposite.