The Hartley transform generalizes to the fractional (FRHT) which gives various uses in different fields of image encryption. Unfortunately, available literature is unable provide its inversion theorem. So accordingly original function cannot retrieve directly, restrict applications. intension this paper propose theorem overcome drawback. Moreover, some properties are discussed paper.

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

Two approaches resulting in two different generalizations of the space-time-fractional advection-diffusion equation are discussed. The Caputo time-fractional derivative and Riesz fractional Laplacian are used. The fundamental solutions to the corresponding Cauchy and source problems in the case of one spatial variable are studied using the Laplace transform with respect to time and the Fourier ...

In this study the general algorithm for the fractionalization of the linear cyclic integral transforms is established. It is shown that there are an infinite number of continuous fractional transforms related to a given cyclic integral transform. The main properties of the fractional transforms used in optics are considered. As an example, two different types of fractional Hartley transform are...

The external description of a system [A,B,C,D] is given by its transfer function W(h). Classically in designing a system with given transfer function the key step is to express W(h) as a linear functional combination of simpler functions. Naturally such a decomposition of a transfer function must correspond to some type of decomposition of the system [A,B,C,D] into smaller subsystems. In this a...

The fractional Fourier transform (FRFT) is a one-parametric generalization of the classical Fourier transform. The FRFT was introduced in the 80th and has found a lot of applications and is now used widely in signal processing. Both the space and the spatial frequency domains, respectively, are special cases of the fractional Fourier domains. They correspond to the 0th and 1st fractional Fourie...