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To describe the time-dependent creep behavior of viscoelastic material, fractional constitutive relation models which are represented by the fractional element networks are studied. Three sets of creep experimental data for polymer and rock are employed to demonstrate the effectiveness of these fractional derivative models. The corresponding constrained problem of nonlinear optimization is solved with an interior-point algorithm to obtain best fitting parameters of these fractional derivative models. The comparison results of measured values and calculated values versus time are displayed through graphics. The results demonstrate that the fractional PoyntingThomson model is optimal in simulating the creep behavior of viscoelastic materials. And it also shows that the interior-point method is effective in the inverse problem to estimate parameters of fractional viscoelastic models.

In this paper, the laser short-pulse heating of a solid surface is considered. The time fractional Cattaneo model is used as the heat conduction model and the corresponding fractional heat conduction equation with a volumetric heat source is built. The analytical solution for the temperature distribution is obtained using the Laplace transformation method. Finally, the numerical results are presented graphically for various values of model parameters, and their effects on the speed of heat conduction propagation are discussed.