Fractional Differentiation and Wavelet Analysis

Abstract

In general we know that there are many basis of L^2 (R) space, in which some can be written in the terms of sin(x) and cos(x). Another way of producing an orthonormal basis from single function involves translations and modulation. In this paper we discuss to construction an orthonormal basis of L^2 (R) from given basis with help of fractional differentiation which is different from parent basis.