A novel viscoelastic modelling of railway track elements and experimental validation

•The FDM (Fractional Derivative Model) with ten parameters is one of the best tool for predicting DMA (dynamical mechanical analysis) experimental results. In a wide frequency range, this model satisfies all data points.•The algorithm based on the Wicked Plot works well. TTSP (Time Temperature Superposition) isn't employed firstly, therefore problems associated with experimental data shifting are avoided.•GMM (Generalized Maxwell Model) can be utilized to represent VE (Visco Elastic) behaviour in a narrow frequency range to reduce FDM (Fractional Derivative Model) time domain computation time. As a result, these parameters can be employed in both analytical and FE solutions with ease.•Numerical solution of Hereditary Integral is implemented into discretized two analytical models via Galerkin method.