Flux and memory measure on net fractals

When the 'residual' memory set is a net fractal set on [0,T], for one case, the connection between the fractional integral and the flux on memory set is established and the approximation of flux on the memory set is obtained. In this case the fractional exponent v only depends on the first similar r ate xi(1) and the first weight P-1 of the (infinite) self-similar measure o n the memory set, but the flux depends on all contractive transforms and al l weights of the (infinite) self-similar measure. For another case, the met hod of getting the approximation of flux is given. The convergent rate of t he Laplace transform of the memory measures is discussed. Some numerical re sults are given. (C) 1999 Published by Elsevier Science B.V. All rights res erved.