Laplace-based method for the linearized dynamical models in the presence of Hilfer fractional operator

The present manuscript examines the role of the Hilfer’s fractional operator on the evolution of three important linearized dynamical models of fluid dynamics. This fractional operator is very special since it interpolates between the two famous fractional derivative operators. The coupling of the Laplace integral transform and the Adomian’s decomposition method is adopted as the methodology. Lastly, the significance of the operator on the evolution of the models is demonstrated graphically for various values of the fractional-order α and type β.