Fractional integrals and fractal structure of memory sets

When the memory set is a fractal, whether the generating mappings of the me mory set are linear or non-linear, a fractional integral approximation of f lux related on the fractal memory set is obtained. The fractional exponent nu is dependent only on the first generating mapping and the first weight o f the self-similar measure. Moreover, a fine approximation of flux in terms of fractional integrals is also obtained. This approximation is dependent on all generating mappings and all weights of self-similar measure. This es tablishes the relationship between the fractional integral and the fractal structure of the memory set. (C) 2000 Elsevier Science B.V. All rights rese rved.