On the Double ARA-Sumudu Transform and Its Applications

Rania Saadeh, Ahmad Qazza () and Aliaa Burqan
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Rania Saadeh: Department of Mathematics, Zarqa University, Zarqa 13132, Jordan
Aliaa Burqan: Department of Mathematics, Zarqa University, Zarqa 13132, Jordan

Mathematics, 2022, vol. 10, issue 15, 1-19

Abstract: The main purpose of this work is to present a new double transform called the double ARA-Sumudu transform (DARA-ST). The application of the new double transform to some basic functions and the master properties are introduced. The convolution and existence theorems are also presented and proved. These new results are implemented to obtain the solution of partial differential equations (PDEs), integral equations (IEs) and functional equations. We obtain new formulas for solving families of PDEs. The latter ones are used to obtain exact solutions of some familiar PDEs such as the telegraph equation, the advection–diffusion equation, the Klein–Gordon equation and others. Moreover, a simple formula for solving a special kind of integral equations is presented and implemented in some applications. The outcomes show that DARA-ST is useful and efficient in handling such kinds of equations.

Keywords: ARA transform; Sumudu transform; partial differential equations; integral equations; functional equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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