A new integral transform on time scales and its applications

Abstract

Integral transform methods are widely used to solve the several dynamic equations with initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform is introduced in this article as a new integral transform on a time scale T to solve a system of dynamic equations. The Sumudu transform on time scale T has not been presented before. The results in this article not only can be applied on 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 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. Finally, we give some applications to illustrate our main results.

The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms

“…Elzaki et al [3,7,8] insists that Elzaki transform ( = 1) should be easily applied to the initial value problems with less computational work and solve the various examples which are not solved by the Laplace or the Sumudu transform. As an application, Agwa et al [9] deal with Sumudu transform on time scales and its applications, Eltayeb and Kilicman [10] have checked some applications of Sumudu one, and Eltayeb et al are highlighting the importance of fractional operators of integral transform and their applications in [11]. The shifted data problems, shifting theorems, and the forms of solutions of ODEs with variable coefficients can be found in [4,12,13].…”

Applications of the Fuzzy Sumudu Transform for the Solution of First Order Fuzzy Differential Equations

“…Furthermore, in [15], the applications of the Sumudu transform on Bessel functions and equations have been explored. The theories and applications of the Sumudu transform have been examined and explored by many authors (see in [16][17][18][19][20][21]). …”

Explicit Solution of Fuzzy Differential Equations by Mean of Fuzzy Sumudu Transform

“…The work on Sumudu transform is then continued by Weerakon [6], [7] who extended the use of Sumudu transform to partial differential equations and later worked on complex inversion formula for Sumudu transform. Later on, various researchers noted the functionality of Sumudu transform and give their effort in building some important basis for Sumudu transform, like theorems and properties [8]- [10].…”