Some Results on a New Refinable Class Suitable for Fractional Differential Problems

In recent years, we found that some multiscale methods applied to fractional differential problems, are easy and efficient to implement, when we use some fractional refinable functions introduced in the literature. In fact, these functions not only generate a multiresolution on R, but also have fractional (non-integer) derivative satisfying a very convenient recursive relation. For this reason, in this paper, we describe this class of refinable functions and focus our attention on their approximating properties.