We study in distributional sense by means of the kernel method an integral transform introduced by Krätzel. It is well known that the cited transform generalizes to the Laplace and Meijer transformation. Properties of analyticity, boundedness, and inversion theorems are established for the generalized transformation. 2000 Mathematics Subject Classification. Primary 44A15, 46F12.

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributiona...

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result o...

Stolt migration is one of the useful GPR imaging algorithms, which has the advantage of fast implementation speed. The fast Fourier transform of integral formula in image reconstruction is realized by coordinate transformation and done through interpolation. Interpolation determines the effectiveness of imaging directly. In the practical applications, zero-fill interpolation in time-domain is u...

A transient quasi-analytic method is improved to analyze the offset reflector for impulse radiating antenna (IRA) applications. Physical optic (PO) approximation and analytic time transform (ATT) are utilized to investigate the time domain (TD) radiating characteristics of the offset reflector. With the appropriate coordinate transformation, the TD far-field integral problem can be simplified t...