Explicit Integral Transform Proofs of Some Transplantation Theorems for the Hankel Transform

1973 ◽  
Vol 4 (2) ◽  
pp. 367-384 ◽  
Author(s):  
Susan Schindler
Keyword(s):  
Integral Transform ◽  
Hankel Transform ◽  
Transplantation Theorems

scholarly journals Matlab code for the Discrete Hankel Transform

2016 ◽  
Author(s):  
Ugo Chouinard ◽  
Natalie Baddour
Keyword(s):  
Fourier Transform ◽  
Numerical Calculation ◽  
Integral Transform ◽  
Hankel Transform ◽  
Matlab Code ◽  
Standard Set

Previous definitions of a Discrete Hankel Transform (DHT) have focused on methods to approximate the continuous Hankel integral transform without regard for the properties of the DHT itself. Recently, the theory of a Discrete Hankel Transform was proposed that follows the same path as the Discrete Fourier/Continuous Fourier transform. This DHT possesses orthogonality properties which lead to invertibility and also possesses the standard set of discrete shift, modulation, multiplication and convolution rules. The proposed DHT can be used to approximate the continuous forward and inverse Hankel transform. This paper describes the Matlab code developed for the numerical calculation of this DHT.

scholarly journals A generalized Hankel transform and its use for solving certain partial differential equations

1999 ◽  
Vol 41 (1) ◽  
pp. 105-117 ◽  
Author(s):  
I. Ali ◽  
S. Kalla
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Integral Transform ◽  
Diffusion Theory ◽  
Ground Surface ◽  
Ground Level ◽  
Hankel Transform ◽  
Partial Differential ◽  
Special Cases

AbstractWe introduce a generalized form of the Hankel transform, and study some of its properties. A partial differential equation associated with the problem of transport of a heavy pollutant (dust) from the ground level sources within the framework of the diffusion theory is treated by this integral transform. The pollutant concentration is expressed in terms of a given flux of dust from the ground surface to the atmosphere. Some special cases are derived.

scholarly journals Matlab code for the Discrete Hankel Transform

2016 ◽  
Author(s):  
Ugo Chouinard ◽  
Natalie Baddour
Keyword(s):  
Fourier Transform ◽  
Numerical Calculation ◽  
Integral Transform ◽  
Hankel Transform ◽  
Matlab Code ◽  
Standard Set

Previous definitions of a Discrete Hankel Transform (DHT) have focused on methods to approximate the continuous Hankel integral transform without regard for the properties of the DHT itself. Recently, the theory of a Discrete Hankel Transform was proposed that follows the same path as the Discrete Fourier/Continuous Fourier transform. This DHT possesses orthogonality properties which lead to invertibility and also possesses the standard set of discrete shift, modulation, multiplication and convolution rules. The proposed DHT can be used to approximate the continuous forward and inverse Hankel transform. This paper describes the Matlab code developed for the numerical calculation of this DHT.

scholarly journals Inversion of the Poisson-Hankel transform

1982 ◽  
Vol 5 (3) ◽  
pp. 485-496
Author(s):  
C. Nasim
Keyword(s):  
Heat Equation ◽  
Initial Temperature ◽  
Differential Operators ◽  
Integral Transform ◽  
Hankel Transform ◽  
Temperature Function ◽  
Generalized Heat Equation

The Poisson-Hankel transform is defined as an integral transform of the initial temperature function, with the kernel as the source solution of the generalized heat equation. In this paper a technique involving integral and differential operators has been used to effect the inversion of the Poisson-Hankel transform.

Solutions to the fractional diffusion-wave equation in a wedge

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Wave Equation ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Neumann Boundary ◽  
Hankel Transform ◽  
Fractional Diffusion ◽  
Polar Coordinates ◽  
Radial Coordinate ◽  
Diffusion Wave ◽  
Angular Coordinate

AbstractThe diffusion-wave equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in polar coordinates in a domain 0 ≤ r < ∞, 0 < φ < φ 0 under Dirichlet and Neumann boundary conditions. The Laplace integral transform with respect to time, the finite sin- and cos-Fourier transforms with respect to the angular coordinate, and the Hankel transform with respect to the radial coordinate are used. The numerical results are illustrated graphically.

scholarly journals Analytical Solutions of the Fractional Mathematical Model for the Concentration of Tumor Cells for Constant Killing Rate

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1156
Author(s):  
Najma Ahmed ◽  
Nehad Ali Shah ◽  
Farman Ali ◽  
Dumitru Vieru ◽  
F.D. Zaman
Keyword(s):  
Mathematical Models ◽  
Cancer Cells ◽  
Tumor Cells ◽  
Analytical Solutions ◽  
Integral Transform ◽  
Hankel Transform ◽  
Transcendental Equation ◽  
Tumor Evolution ◽  
Radial Coordinate ◽  
Positive Roots

Two generalized mathematical models with memory for the concentration of tumor cells have been analytically studied using the cylindrical coordinate and the integral transform methods. The generalization consists of the formulating of two mathematical models with Caputo-time fractional derivative, models that are suitable to highlight the influence of the history of tumor evolution on the present behavior of the concentration of cancer cells. The time-oscillating concentration of cancer cells has been considered on the boundary of the domain. Analytical solutions of the fractional differential equations of the mathematical models have been determined using the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The positive roots of the transcendental equation with Bessel function J0(r)=0, which are needed in our study, have been determined with the subroutine rn=root(J0(r),r,(2n−1)π/4,(2n+3)π/4),n=1,2,… of the Mathcad 15 software. It is found that the memory effects are stronger at small values of the time, t. This aspect is highlighted in the graphical illustrations that analyze the behavior of the concentration of tumor cells. Additionally, the concentration of cancer cells is symmetric with respect to radial angle, and its values tend to be zero for large values of the time, t.

scholarly journals The H-function transform

1970 ◽  
Vol 11 (2) ◽  
pp. 142-148 ◽  
Author(s):  
K. C. Gupta ◽  
P. K. Mittal
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Integral Transform ◽  
Applied Mathematics ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Stieltjes Transform ◽  
Special Cases ◽  
Mathematics And Physics

Here we introduce a new integral transform whose kernel is the H-function. Since most of the important functions occurring in Applied Mathematics and Physics are special cases of the H-function, various integral transforms involving these functions as kernels follow as special cases of our transform. We mention some of them here and observe that a study of this transform gives general and useful results which serve as key formulae for several important integral transforms viz. Laplace transform, Hankel transform. Stieltjes transform and the various generalizations of these transforms. In the end we establish an inversion formula for the new transform and point out its special cases which are generalizations of results found recently.

\Transient Heat Diffusion Problems with Variable Thermal Properties Solved by Generalized Integral Transform Technique

2014 ◽  
Vol 8 (5) ◽  
pp. 931
Author(s):  
Marcelo Ferreira Pelegrini ◽  
Thiago Antonini Alves ◽  
Ricardo Alan Verdú Ramos ◽  
Cassio Roberto Macedo Maia
Keyword(s):  
Thermal Properties ◽  
Integral Transform ◽  
Heat Diffusion ◽  
Transient Heat Diffusion ◽  
Integral Transform Technique ◽  
Diffusion Problems

AN INTEGRAL TRANSFORM APPLICATION TO MIXED CONVECTION IN LAMINAR FLOW BETWEEN INCLINED PARALLEL PLATES

2001 ◽  
Vol 3 (2-3) ◽  
pp. 16
Author(s):  
Rogerio Ramos ◽  
Jesus Salvador Perez Guerrero
Keyword(s):  
Laminar Flow ◽  
Mixed Convection ◽  
Integral Transform ◽  
Parallel Plates
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