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.