  In this article, we propose an exponential B-spline collocation method to
approximate the solution of the fractional sub-diffusion equation of Caputo
type. The present method is generated by use of the
Gorenflo-Mainardi-Moretti-Paradisi (GMMP) scheme in time and an efficient
exponential B-spline based method in space. The unique solvability is
rigorously discussed. Its stability is well illustrated via a procedure closely
resembling the classic von Neumann approach. The resulting algebraic system is
tri-diagonal that can rapidly be solved by the known algebraic solver with low
cost and storage. A series of numerical examples are finally carried out and by
contrast to the other algorithms available in the literature, numerical results
confirm the validity and superiority of our method.
