A new method of solving Bessel's differential equation using the -transform

Parseval–Goldstein type identities involving the ℒ4-transform and the 𝒫4-transform and their applications

“…We conclude by remarking that many other infinite integrals can be evaluated in this manner by applying the Lemma as well as the Theorem and its corollaries considered here (see also [16], [17] and [18]). …”

“…Remark 2 Alternatively, we can calculate the P 4 -transform in (39) by using the relationship (17) and the known formula [11, Vol. 2, p. 225, Entry (10)].…”

An inversion technique for l_2-transform with applications

“…The δ -derivative operator can be successively applied in a similar fashion for any positive integer power. Theorem2.1: 1) are all continuous functions with a piecewise continuous derivative f (n) on the interval t ≥ 0 and if all functions are of exponential order exp(c 2 t 2 ) as t → ∞ for some constant c then, [ 2 ] 1.…”

Applications of the L_2-Transform to Partial Differential Equations

“…Alternatively, the Laplace transform has applications to physics in the analysis of linear-time invariant systems, like electrical circuits and mechanical systems. The L 2 -transform already has some well understood applications to classical ordinary differential equations such as Bessel's differential equation [2] (Yurekli, Wilson (2002)) and Hermite's differential equation [3] (Yurekli, Wilson (2003)). The goal of this article is to illustrate the applicability of the L 2 -transform to solving certain partial differential equations-an application of the L 2 -transform never before examined in literature.…”