The method of partial Fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the Tricomi operator. In proving these results, we establish explicit formulas for Fourier transforms of some functions involving Bessel functions.

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. In this paper, we will introduce sev...

Generalized Discrete Fourier Transform (GDFT) with non-linear phase is a complex valued, constant modulus orthogonal function set. GDFT can be effectively used in several engineering applications, including discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communication systems. The constant modulus transforms like discrete Fou...

In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again for a fixed vector in the image space, ...

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.

In this paper we establish some new exact solutions regarding to the unsteady flow of a generalized Oldroyd-B fluid produced by a suddenly moved plate between two side walls perpendicular to the plate. The governing equation has been obtained through fractional calculus approach. Fourier sine transform and discrete Laplace transform have been used to obtained exact solutions. The solution of ve...

The discrete evolutionary transform is applied to signals in a blind–way without any signal parameters. For this reason, discrete evolutionary transform is not optimal and needs an improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform. We redefine the generalized timebandwidth product optimal short–time Fourier t...