Exact solutions for some time-fractional evolution equations using Lie group theory

In this paper, some classes of nonlinear partial fractional differential equations arising in some important physical phenomena are considered. Lie group method is applied to investigate the symmetry group of transformations under which the governing time-fractional partial differential equation remains invariant. The symmetry generators are used for constructing similarity variables, which leads to a reduced ordinary differential equation of Erdelyi-Kober fractional derivatives. Furthermore, a particular exact solution for each governing equation(s) is constructed. Moreover, the physical significance of the solution is investigated graphically based on numerical simulations in order to highlight the importance of the study.