A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically...

We propose a new method for analysis of the sampling and reconstruction conditions of signals by use of the multiple-parameter fractional Fourier transform (MPFRFT). It is shown that the MPFRFT may provide a novel understanding of sampling process. The proposed sampling theorem generalizes classical Shannon sampling theorem and Fourier series expansion, and provides a fullreconstruction procedu...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...