Abstract

In this paper, we perform a Lie symmetry analysis of time-fractional Bagley–Torvik (TF-BT) equation by employing Caputo fractional derivatives. The TF-BT equation describes the time response of viscoelastic materials with taking into account memory effects. The Lie symmetry method is used to find the symmetry generators, invariant solutions, symmetry reductions, and conservation laws. Symmetry reductions provide exact similarity solutions, where the admitted symmetry group follows from a prolongation of fractional derivative structure. Even without a classical Lagrangian, conservation laws can then be derived from Ibragimov’s theorem. Lie symmetry analysis is a useful technique for fractional differential equations, as demonstrated by the analytical solutions of the TF-BT problem that are obtained and fulfill this equation.