Lie Algebra and Conservation Laws for the Time-fractional Heat Equation

The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that that the numbers of symmetries and Lie brackets are reduced significantly as compared to the nonfractional order for all the dimensions. In fact for integer order linear heat equation the number of solution symmetries is equal to the product of the order and space dimension, whereas for the fractional case, it is half of the product on the order and space dimension. We have classified the symmetries and discussed the Lie algebras and conservational laws. We generalise the number of symmetries to the n-dimensional heat equation.