Fractional Lienard type model of a pipeline within the fractional derivative without singular kernel

Abstract

This paper presents the procedure to obtain analytical solutions of Li,nard type model of a fluid transmission line represented by the Caputo-Fabrizio fractional operator. For such a model, we derive a new approximated analytical solution by using the Laplace homotopy analysis method. Both the efficiency and the accuracy of the method are verified by comparing the obtained solutions with the exact analytical solution. Good agreement between them is confirmed.