Stability and symmetry analysis of the time-fractional McKendrick equation

Abstract

In this paper, we apply the Lie symmetries analysis to obtain the infinitesimal generators admitted by the time fractional Riemann-Liouville McKendrick equation. We will show that the reduction via the Erdélyi-Kober fractional operator allows us to construct some exact solutions by using the power series approach. Moreover, the exploitation of the stability of the symmetry algebra allowed us to construct a new family of exact solutions. Based on the obtained infinitesimal generators and the use of Ibragimov's method, we build conservation quantities of the studied equation. Finally, 3D plots are provided to illustrate the behavior of the derived solutions for specific parameter values.