The non-integer operation associated to random variation sets of the self-similar set

When memory sets are random variation sets of the self-similar set and the total number of remaining states in each stage of the division of this set is normalized to unity, the corresponding flux and fractional integral are "robust" and stable under some conditions. This answers an open problem pro posed by Alian Le Mehaute et ar. in their book entitled Irreversibilite Tem porel et Geometrie Fractale. (C) 2000 Elsevier Science B.V. All rights rese rved.