Showing papers on "Hartley transform published in 2023"
TL;DR: In this article , the double Aboodh-Shehu transform was used to solve a linear partial differential equation with unknown function of two independent variables, which can then be solved by the formal rules of algebra.
Abstract: Abstract
We combine the Aboodh transform and Shehu transform to give another double transform which is called the double Aboodh-Shehu transform. This interesting transform reduces a linear partial differential equation with unknown function of two independent variables to an algebraic equation, which can then be solved by the formal rules of algebra, or by applying the double Aboodh-Shehu transform directly to the given equation.
TL;DR: In this paper , a new integral transform for functions of exponential order called NE integral transform is introduced and some applications of the NE- transform to find the solution to ordinary linear equation are given.
Abstract: Abstract This work introduces a new integral transform for functions of exponential order called “NE integral transform”. We prove some properties of NE -transform. Also, some applications of the NE- transform to find the solution to ordinary linear equation are given. The relationships of the new transform with well-known transforms are characterized by integral identities. We study the properties of this transform. Then we compare it with few exiting integral transforms in the Laplace family such as Laplace, Sumudu, Elzaki, Aboodh and etc. As well, the NE integral transform is applied and used to find the solution of linear ordinary differential equations.
10 Apr 2023
TL;DR: In this article , the Fourier transform associated with the differential operator is studied, which in addition to the continuous part of the spectrum that defines this transform, may contain a set of eigenfunctions.
Abstract: Most of the known Fourier transforms associated with the equations of mathematical physics have a trivial kernel, and an inversion formula as well as the Parseval equality are fulfilled. In other words, the system of the eigenfunctions involved in the definition of the integral transform is complete. Here we will study Fourier transform associated with the differential operator, which in addition to the continuous part of the spectrum that defines this transform, may contain a set of eigenfunctions. These functions become the elements of the kernel of Fourier transform.
TL;DR: In this paper , a spherical linear canonical transform in spherical polar coordinates is proposed, which is based on the spherical Fourier transform and spherical linear Hankel transform, and several essential properties of the proposed transform are obtained, including linearity, inversion formulas, shifts and convolution theorems.
TL;DR: In this paper , a new integral type transformation is introduced, which is the generalization of Laplace and Fourier transform, named as "Fareeha transform", which is successfully applied on ordinary differential equation to show its efficacy and simplicity.
Abstract: In this paper, a new integral‐type transformation is being introduced, which is the generalization of Laplace and Fourier transform. This integral transform is named as “Fareeha transform.” It is successfully applied on ordinary differential equation to show its efficacy and simplicity. Also, the possible applications of Fareeha transform in control theory, electric circuits, and data compression have been discussed in detail.
TL;DR: In this paper , an extended fractional Mellin transform in the generalized sense is considered and inversion formula is investigated by using inversion of classical Mellin Transform and prove Parseval"s Identity for an Extended fractional MTL.
Abstract: Integral transform is one of the techniques in the function transformation methods. Integral transforms have been interesting tools for solving different problems arising in applied mathematics, mathematical physics and engineering science for at least two centuries. We have studied an extended fractional Mellin transform in the generalized sense. For this testing space E and its dual space E* are considered. We have investigated inversion formula by using inversion of classical Mellin transform and prove Parseval"s Identity for an extended fractional Mellin transform. Also discussed some results of this transform.
TL;DR: In this article , the authors proposed inversion theorem of fractional Hartley transform (FRHT) to overcome the drawback of the available literature of FRHT, which cannot retrieve the original function directly, which restricts its applications.
Abstract: The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion theorem. So accordingly original function cannot retrieve directly, which restrict its applications. The intension of this paper is to propose inversion theorem of fractional Hartley transform to overcome this drawback. Moreover, some properties of fractional Hartley transform are discussed in this paper.
TL;DR: In this article , a novel octonion special affine Fourier transform (O−SAFT) was introduced and several uncertainty inequalities for the proposed transform were established. But the authors focused on the norm split and energy conservation properties.
Abstract: The special affine Fourier transform (SAFT) is an extended version of the classical Fourier transform and incorporates various signal processing tools which include the Fourier transforms, the fractional Fourier transform, the linear canonical transform, and other related transforms. This paper aims to introduce a novel octonion special affine Fourier transform (O−SAFT) and establish several classes of uncertainty inequalities for the proposed transform. We begin by studying the norm split and energy conservation properties of the proposed (O−SAFT). Afterwards, we generalize several uncertainty relations for the (O−SAFT) which include Pitt’s inequality, Heisenberg–Weyl inequality, logarithmic uncertainty inequality, Hausdorff–Young inequality, and local uncertainty inequalities. Finally, we provide an illustrative example and some possible applications of the proposed transform.