Equations between the differential order and the maximum of the fractional-order differential for the specified peak signals are developed based on the variation of the maximum of the specified peak signals at different orders.

A fractional-order differentiation filter is designed to obtain fractional-order differential of a given signal and to simplify computation of the fractional-order differential.

Image enhancement for rock fractures based on fractional differential

The theoretical analysis shows that fractional differentials can greatly increase high frequency,reinforce medium frequency and non-linearly preserve low frequency of signals,hence they could be used for edge and texture enhancement as well as smooth area preservation.

In order to improve signal noise ratio(SNR) of edge extraction,and to detect edge more effectively and exactly,according to fractional order differential difference function which was deduced from classical fractional differential G-L definition,an approximate fractional order differential Tiansi module was constructed.

We examine the properties and applications of the Riemann fractional integral and derivative,and give the new definitions of left-sided fractional derivative and right-sided fractional derivative.

In this paper,we extend the total variation model for image denoising is which based on gradient to a new model based on fractional derivative,and then making use of the characteristic that fractional derivative and convolution integral have the same discrete formula in certain situation,We propose a variational model based on convolution integral which can be computed easily.