A Modified and a Finite Index Weber Transforms

In this research paper, we discuss new class of integral transform whose kernel involved a product of exponential function and I-function of two variables defined by K. Shantha Kumari, Vasudevan Nambisan and A.K. Rathie [2]. In the last particular cases of two dimensional integral transform are also discussed.

Journal of Engineering Physics and Thermophysics

Analysis Mathematica, 1997

An integral transform of generalized functions. II ANIL KUMAR MAHATO D(I) will denote the standard union space (see [7, pp. 32, 33]) of countably multinormed spaces DK (I) of all complex-valued smooth functions defined on I = (0, c¢), which vanish on those points of I that are not in a compact subset K of I, with seminorms defined by ~k(¢) = suplDkC(t)l, ¢ ~ DK(I), tEI k c¢ and with the topology generated by the countable multinorms {7 }k=0 assigned to the corresponding linear space with usual pointwise operations of addition and multiplication of functions. E(I) denotes the space of smooth functions on I. Its dual E'(I) is the space of distributions with compact support on I.

Sibirskie Elektronnye Matematicheskie Izvestiya, 2021

In this paper we apply the Integral Transforms Composition Method (ITCM) in order to derive compositions of integral transforms with Bessel functions in kernels, and obtain norm estimates and other properties of such composition transforms. Exactly, we consider transmutations which are compositions of classical Hankel and Y integral transforms. Norms estimates in L2 for these integral transforms with Bessel functions in kernels and their compositions are obtained. Also boundedness conditions for such transforms in weighted Lebesgue classes are proved. Classical integral transforms are used in this method as basic blocks. The ITCM and transmutations obtained by this method are applied to deriving connection formulas for solutions of singular dierential equations.

Boletim da Sociedade Paranaense de Matemática, 2022

Objective of this study is to give a shape of general integral transform for studying its convergence in the general set-up, from which convergences of some well know integral transforms follow easily as well as these integral transforms appear as particular cases of the present integral transform; some more may appear as new but special cases of present transform which have been listed but not studied here.

2010

In this study, we apply double integral transforms to solve partial differential equation namely double Laplace and Sumudu transforms, in particular the wave and poisson's equations were solved by double Sumudu transform and the same result can be obtained by double Laplace transform.

Gazi University Journal of Science

In this paper, Parseval-Goldstein type theorems involving the G ̃n-integral transform which is modified from G_2n-integral transform [7] and the -integral transform [8] are examined. Then, theorems in this paper are shown to yield a number of new identities involving several well-known integral transforms. Using these theorems and their corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Generalizations of Riemann-Liouville and Weyl fractional integral operators are also defined. Some theorems relating generalized Laplace transform, generalized Widder Potential transform, generalized Hankel transform and generalized Bessel transform are obtained. Some illustrative examples are given as applications of these theorems and their results.

2018

In this paper, the generalization of integral transform (GIT) of the function G{f(t)} is introduced for solving both the differential and interodifferential equations. This transform generalizes the integral transforms which use exponential functions as their kernels and the integral transform with polynomial function as a kernel. The generalized integral transform converts the differential equation into us domain (the transformed variables) and reconverts the result by its inverse operator. In particular, if u = 1, then the generalized integral transform coincides with the Laplace transform and this result can be written in another form as the polynomial integral transform. 2010 Mathematics Subject Classifications: 44B53, 44B54

Cornell University - arXiv, 2022

In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence theorem, the scaling property, elimination property a Parseval-type identity, and inversion formula. The relationships of the new transform with well-known transforms are characterized by integral identities. The new transform is applied to solve certain initial boundary value problems. Some illustrative examples are given. The results established in this work extend and generalize recently published results.

Mathematics

A new Weber-type integral transform and its inverse are defined for the representation of a function f(r,t), (r,t)∈[R,1]×[0,∞) that satisfies the Dirichlet and Robin-type boundary conditions f(R,t)=f1(t), f(1,t)−α∂f(r,t)∂r|r=1=f2(t), respectively. The orthogonality relations of the transform kernel are derived by using the properties of Bessel functions. The new Weber integral transform of some particular functions is determined. The integral transform defined in the present paper is a suitable tool for determining analytical solutions of transport problems with sliding phenomena that often occur in flows through micro channels, pipes or blood vessels. The heat conduction in an annular domain with Robin-type boundary conditions is studied. The subroutine “root(⋅)” of the Mathcad software is used to determine the positive roots of the transcendental equation involved in the definition of the new integral transform.