Multi-dimensional Laplace transforms and systems of partial differential equations

Towards new general double integral transform and its applications to differential equations

“…Recently, double Laplace transform is used extensively to solve partial differential equations with unknown functions of two variables which obtained good results compared to numeric methods. 3,[17][18][19][20][21] Moreover, there exist in literature further extensions of double Laplace transform like double Sumudu transform, [22][23][24][25][26][27] double Shehu transform, 28 double Elzaki transform, 29 and double Ramadan group integral transform. 30 In 2020, the second and third authors have introduced new general integral transforms independently which are almost similar.…”

An Identity for Two Integral Transforms Applied to the Uniqueness of a Distribution via its Laplace-Stieltjes Transform

“…Another related integral transform of functions is the conventional Laplace transform which is a powerful tool in solving systems of both ordinary and partial differential equations through the uniqueness theorem -Lerch's Theorem (see Theorem A below, Aghili andParsa Moghaddam 2011, or van der Pol andBremmer 1955). In this paper, we prove the identity for the Laplace-Stieltjes and the Laplace-Carson transforms of a distribution function (the latter is in terms of the conventional Laplace transform; see Theorems E, F and 4).…”

New trends in Laplace type integral transforms with applications

“…The authors have already studied several methods to evaluate series, integrals and solve fractional differential equations, specially the popular Laplace transform method, [1], [2], [3], [4], [5], [6], [7], [8] and this work is a completion for their previous researches. Proof: See [14].…”