Scaling relation equation is newly introduced to model the random walk in the presence of the space-time fractal. It is found out that the various transpost regimes including the anomalous transport exist accordinding to the magnitude of the fractal constants.This result is shown to be very similar to the conclusion derived within the KBS model. Multifractal generalization of the above formalism is suggested and applied to the problem of the coexistence of the accelerating and the localizing island.It is shown that the same results as the velocity model are obtained.Also, I have generalized the Gelsel's Renewal theory to the case of nonconstant velocity and the multifractal situation.The result obtained within the generalized Renewal theory is shown to be identical to that within the fractal random walk theory which is the above CTRW theory accompanied by the scaling relation assumption.The simplified derivation of the fractional kinetic equation is considered and I have suggeated the functional form satisfying the scaling relation assumption.This theoretical result is tested by the numerical simulation carried out on the Seesaw(Toggle) mapping which describes the banana motion of the charged particles in Tokamak.At a certain particular value of the control parameter the phase space is shown to be characterized by the accelerating island which contains cxact self-similar chaos border.It is found out that the numerical simulation results confirm the validity of the theoretical consideration.In summary, it can be concluded that the fine fractal property near the chaos border determines the global transport character.In this paper this is considered by the new theoretical methods.
