In this talk, we propose projection methods for solving fractional Volterra integro-differential equation
(FVIDE) with a smooth kernel. Using property of Caputo fractional derivative, the governing
equation is reformulated into a system of FVIDEs. Further, the reformulated system is transformed
into a system of fractional Fredholm integro-differential equations using a variable transformation.
With this, we obtain improved convergence rate using iterated Galerkin method. Moreover, superconvergence
results are obtained using multi-Galerkin and iterated multi-Galerkin methods. Theoretical
and numerical analysis shows that the order of convergence increases with increasing the order of
fractional derivative. Numerical problems are provided to validate theoretical results.