Mollification of the Gibbs phenomena using orthogonal wavelets

In a preceding paper, we study the use of the wavelet expansion in terms of rapidly decaying wavelet, which is Meyer´s wavelet, to the problem of mollification in the numerical calculation of the fractional derivative of a function involving noise. In the present paper, we study the problem of depressing the oscillation due to the Gibbs phenomenon, by applying the above method of mollification.