A new integral transform and associated distributions

Abstract

In this paper, we generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

“…Further, in Eltayeb et al [46], the Sumudu transform was extended to the distributions and some of their properties were also studied in Kılıçman and Eltayeb [47]. Recently, this transform is applied to solve the system of differential equations; see Kılıçman et al in [48].…”

A new integral transform on time scales and its applications

“…The results in this article not only can be applied to ordinary differential equations when T = R, difference equations when T = N 0 , but also, can be applied for q-difference equations when T = q N 0 , where q N 0 := {q t : t ∈ N 0 for q > 1} or T = q Z := q Z ∪ {0} for q>1 which has several important applications in quantum theory and on different types of time scales like T = hN 0 , T = N 2 0 , and T = T n the space of the harmonic numbers. Regarding the comparison between Sumudu and Laplace transform, see for example, [4][5][6][7]16]. For example when T = R, Maxwell's equations were solved for transient electromagnetic waves propagating in lossy conducting media, see [16] where the Sumudu transform of Maxwell's differential equations yields a solution directly in the time domain, which neutralizes the need to perform the inverse Sumudu transform.…”

“…By looking at the properties of this transform one can notice that the Sumudu transform has very special and useful properties and it can help with intricate applications in the sciences and engineering. For example, in [5], the Sumudu transform was extended to distributions (generalized functions) and some of their properties were also studied in [6,7]. Recently Kılıçman et al applied this transform to solve a system of differential equations, see [8].…”

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

“…For more information and properties of Sumudu transform and its derivatives, [14][15][16][17][18][19]. Actually one can simply prove that there is a big connection between double Sumudu and double Laplace transforms.…”