In this paper, the homotopy decomposition method with a modified definition of beta fractional derivative is adopted
to find approximate solutions of higher-dimensional time-fractional diffusion equations. To apply this method, we find
the modified beta integral for both sides of a fractional differential equation first, then using homotopy decomposition
method we can obtain the solution of the integral equation in a series form. We compare the solutions obtained by the
proposed method with the exact solutions obtained using fractional variational homotopy perturbation iteration method
via modified Riemann-Liouville derivative. The comparison shows that the results are in a good agreement.