Fundamental solutions and conservation laws for conformable time fractional partial differential equation

Abstract

In this paper, the connections between fundamental solutions and Lie symmetry groups for a class of conformable time fractional partial differential equations (PDEs) with variable coefficient are investigated for the first time. The group-invariant solutions to the considered equations are constructed by means of symmetry group method. Then, the corresponding fundamental solutions for these PDEs are established by taking the inverse Laplace transform of the group invariant solutions. In addition, some examples are introduced to illustrate the effectiveness of this approach. Furthermore, the conservation laws of these fractional PDEs are obtained making use of new Noether theorem.