Theis’ theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula this certain integral transform H[g](r,t) of pumping function g that depends on time t relative position r point as well other physical parameters. Several analytic approximations have been investigated literature are valid accurate ...

Abstract The current paper is about the investigation of a new integral transform introduced recently by Jafari. Specifically, we explore applicability this on Atangana–Baleanu derivative and associated fractional integral. It shown that applying specific conditions transform, other transforms are deduced. We provide examples to reinforce transform.

The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter ρ > 0. In previous work a convenient form of the inverse transformation was derived for the case ρ = 3/2. This paper generalizes that result to all ρ > 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iter...

The generalized Funk transform is a integral transform acting from densities on a manifold X to functions defined on a family Σ of hypersurfaces in X. The dual operator M is again a Funk transform which is defined for densities on the manifold Σ. We state twoside estimates for the operator M and a description of the range of the Funk transform operatorM and approximation theorem for the kernel ...

The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GF...