  We consider a time fractional differential equation of order $\alpha$,
$0<\alpha<1$, $$ \frac{\partial c(x,t)}{\partial
t}={}^C_0\mathcal{D}_t^{\alpha}[(Ac)(x,t)]+q(x,t) ,\quad x > 0, t > 0, \quad
c(x,0)=f(x). $$ where ${}^C_0\mathcal{D}_t^{\alpha}$ is the Caputo fractional
derivative of order $\alpha$, $A$ is a linear differential operator, $q(x,t)$
is a source term, and $f(x)$ is the inital condition. Approximate (truncated)
series solutions are obtained by means of the Variational Iteration Method
(VIM). We find the series solutions for different cases of the source term, in
a form that is readily implementable on the computer where symbolic computation
platform is available. The error in truncated solution $c_n$ diminishes
exponentially fast for a given $\alpha$ as the number of terms in the series
increases. VIM has several advantages over other methods that produce solutions
in the series form. The truncated VIM solutions often converge rapidly
requiring only a few terms for fast and accurate approximations.
