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

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