The analytical solution of the partial differential equation with time- and space-fractional derivatives was derived by means of the homotopy decomposition method (HDM). Some examples are given and comparisons are made. The evaluations show that the homotopy decomposition method is extremely successful and suitable. The achieved results make the steadfastness of the HDM and its wider applicability to fractional differential equation obvious. Additionally, the adding up implicated in HDM is exceptionally undemanding and uncomplicated. It is confirmed that HDM is an influential and professional apparatus for FPDEs. It was also established that HDM is supplementary well organized than the ADM, VIM, HAM, and HPM.