A fractional wavelet Galerkin method for the fractional diffusion problem

The aim of this paper is to solve some fractional differential problems hav- ing time fractional derivative by means of a wavelet Galerkin method that uses the fractional scaling functions introduced in a previpous paper as approximating functions. These refinable functions, which are a generalization of the fractional B-splines, have many interesting approximation properties. In particular, their fractional derivatives have a closed form that involves just the fractional difference operator. This allows us to construct accurate and efficient numerical methods to solve fractional differential problems. Some numerical tests on a fractional diffusion problem will be given.