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We consider a time fractional differential equation of order $\alpha$,$0<\alpha<1$, $$ \frac{\partial c(x,t)}{\partialt}={}^C_0\mathcal{D}_t^{\alpha}[(Ac)(x,t)]+q(x,t) ,\quad x > 0, t > 0, \quadc(x,0)=f(x). $$ where ${}^C_0\mathcal{D}_t^{\alpha}$ is the Caputo fractionalderivative 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, ina form that is readily implementable on the computer where symbolic computationplatform is available. The error in truncated solution $c_n$ diminishesexponentially fast for a given $\alpha$ as the number of terms in the seriesincreases. VIM has several advantages over other methods that produce solutionsin the series form. The truncated VIM solutions often converge rapidlyrequiring only a few terms for fast and accurate approximations.

Approximate solutions of a time-fractional diffusion equation with a source term using the variational iteration method