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Analysis of Implementation of Differential Equations of Non-Integer Orders to Dual-Phase-Lag Model Approximation

This paper includes an analysis of a possibility of implementation of fractional differential equations in order to approximate the Dual-Phase-Lag heat transfer model. Due to this fact, the order of the time derivative, existing in classical Fourier-Kirchhoff equation, is being changed to the non-integer one based on the Grünwald-Letnikov fractional derivative definition. Then, the obtained normalized temperature rises are compared with these ones received using the Dual-Phase-Lag model. Based on yielded temperature distributions, the fractional time derivative orders are fitted to different pairs of the temperature and heat flux time lags, being the parameters of Dual-Phase-Lag model. Finally, the formula combining the value of the time derivative order with both time lag values is delivered and a new approximation of Dual-Phase-Lag model is proposed.