Browsing by Author "Al-Omari, Shrideh Khalaf Qasem"

Now showing 1 - 7 of 7

A Lebesgue İntegrable Space of Boehmians for A Class of Dk Transformations
(Eudoxus Press, 2018) Baleanu, Dumitru; Al-Omari, Shrideh Khalaf Qasem; 56389
Boehmians are objects obtained by an abstract algebraic construction similar to that of field of quotients and it in some cases just gives the field of quotients. As Boehmian spaces are represented by convolution quotients, integral transforms have a natural extension onto appropriately defined spaces of Boehmians. In this paper, we have defined convolution products and a class of delta sequences and have examined the axioms necessary for generating the Dk spaces of Boehmians. The extended Dk transformation has therefore been defined as a one-to-one onto mapping continuous with respect to Δ and δ convergences. Over and above, it has been asserted that the necessary and sufficient conditions for an integrable sequence to be in the range of the Dk transformation is that the class of quotients belongs to the range of the representative. Further results related to the inverse problem are also discussed.
A Quadratic-Phase Integral Operator for Sets of Generalized Integrable Functions
(John Wiley and Sons LTD., 2020) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, we aim to discuss the classical theory of the quadratic-phase integral operator on sets of integrable Boehmians. We provide delta sequences and derive convolution theorems by using certain convolution products of weight functions of exponential type. Meanwhile, we make a free use of the delta sequences and the convolution theorem to derive the prerequisite axioms, which essentially establish the Boehmian spaces of the generalized quadratic-phase integral operator. Further, we nominate two continuous embeddings between the integrable set of functions and the integrable set of Boehmians. Furthermore, we introduce the definition and the properties of the generalized quadratic-phase integral operator and obtain an inversion formula in the class of Boehmians.
Convolution theorems associated with some integral operators and convolutions
(Taylor&Francis LTD, 2019) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this article, various convolution theorems involving certain weight functions and convolution products are derived. The convolution theorems we obtain are more general, convenient, and efficient than the complicated convolution theorem of the Hartley transform. Further results involving new variants of generalizations of Fourier and Hartley transforms are also discussed.
On generalized space of quaternions and its application to a class of Mellin transforms
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; Baleanu, Dumitru; 56389
The Mellin integral transform is an important tool in mathematics and is closely related to Fourier and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set of generalized functions. Then we provide a new definition of the cited Mellin integral on the provided set of quaternions. The attributive Mellin integral is one-to-one, onto and continuous in the quaternion spaces. Further properties of the discussed integral are given on a quaternion context. (C) 2016 All rights reserved.
On the generalized stieltjes transform of Fox's Kernel function and its properties in the space of generalized functions
(Eudoxus Press, 2017) Baleanu, Dumitru; Baleanu, Dumitru; 56389
In this paper, a Stieltjes transform enfolding some Fox's H-function has been investigated on certain class of generalized functions named as Boehmians. By developing two spaces of Boehmians, the extended transform has been inspected and some general properties are also obtained. An inverse problem is also discussed in some detail.
Quaternion fourier integral operators for spaces of generalized quaternions
(Wiley, 2018) Baleanu, Dumitru; Baleanu, Dumitru; 56389
This article aims to discuss a class of quaternion Fourier integral operators on certain set of generalized functions, leading to a method of discussing various integral operators on various spaces of generalized functions. By employing a quaternion Fourier integral operator on points closed to the origin, we introduce convolutions and approximating identities associated with the Fourier convolution product and derive classical and generalized convolution theorems. Working on such identities, we establish quaternion and ultraquaternion spaces of generalized functions, known as Boehmians, which are more general than those existed on literature. Further, we obtain some characteristics of the quaternion Fourier integral in a quaternion sense. Moreover, we derive continuous embeddings between the classical and generalized quaternion spaces and discuss some inversion formula as well.
Some results for Laplace-type integral operator in quantum calculus
(Springer Open, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Purohit, Sunil D.; 56389
In the present article, we wish to discuss q-analogues of Laplace-type integrals on diverse types of q-special functions involving Fox's H-q-functions. Some of the discussed functions are the q-Bessel functions of the first kind, the q-Bessel functions of the second kind, the q-Bessel functions of the third kind, and the q-Struve functions as well. Also, we obtain some associated results related to q-analogues of the Laplace-type integral on hyperbolic sine (cosine) functions and some others of exponential order type as an application to the given theory.