In this article, we define the fractional Mellin transform by using Riemann-Liouville fractional integral operator and Caputo fractional derivative of order [Formula: see text] and study some of their properties. Further, some properties are extended to fractional way for Mellin transform.

The fractional cosine and sine transforms – closely related to the fractional Fourier transform, which is now actively used in optics and signal processing, and to the fractional Hartley transform – are introduced and their main properties and possible applications as elementary fractional transforms of causal signals are discussed.

Abstract The integral transform method based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the generalized Weyl space-fractional operator. The solutions, representing ...

The wavelet transform, which has had a growing importance in signal and image processing, has been generalized by association with both the wavelet transform and the fractional Fourier transform. Possible implementations of the new transformation are in image compression, image transmission, transient signal processing, etc. Computer simulations demonstrate the abilities of the novel transform....

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of fourdimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results ...

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.

In this article we provide integral representations for the Dirichlet beta and Riemann zeta functions, which are obtained by combining Mellin transform with the fractional Fourier transform. As an application of these integral formulas we derive tractable expansions of these L-functions in the series of Meixner-Pollaczek polynomials and rising factorials.

Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative filters inserted between appropriately scaled ordinary Fourier transform stages. Thus every operation that can be accomplished by repeated filtering in fractional Fourier domains can a...

In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical examples clearly indicates superior discrimination performance. Ó 2001 Published by Elsevier Science B.V.