A wavelet Galerkin-collocation method for a fractional diffusion equation.

In this talk we present a wavelet method to solve the fractional-in-time differential diffusion problem The proposed method combines a wavelet collocation method in time and a wavelet Galerkin method in space that use the fractional wavelets associated to the fractional refinable func- tions introduced from Laura Pezza in 2007 as approximating functions. The main advantage is in that both fractional and integer order derivatives of the fractional wavelets can be evaluated by a closed form that involves just the fractional difference operator. We will show the effectiveness and efficiency of the method by some numerical tests.