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On the Double ARA-Sumudu Transform and Its Applications

Author

Listed:
  • Rania Saadeh

    (Department of Mathematics, Zarqa University, Zarqa 13132, Jordan)

  • Ahmad Qazza

    (Department of Mathematics, Zarqa University, Zarqa 13132, Jordan)

  • Aliaa Burqan

    (Department of Mathematics, Zarqa University, Zarqa 13132, Jordan)

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.

Suggested Citation

  • Rania Saadeh & Ahmad Qazza & Aliaa Burqan, 2022. "On the Double ARA-Sumudu Transform and Its Applications," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2581-:d:871075
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    References listed on IDEAS

    as
    1. Shams A. Ahmed & Tarig M. Elzaki & Abdelgabar Adam Hassan, 2020. "Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform)," Abstract and Applied Analysis, Hindawi, vol. 2020, pages 1-7, October.
    2. Ahmad Qazza & Aliaa Burqan & Rania Saadeh, 2021. "A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    3. Abdon Atangana & Adem Kilicman, 2013. "A Novel Integral Operator Transform and Its Application to Some FODE and FPDE with Some Kind of Singularities," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, August.
    4. Hassan Eltayeb, 2013. "Note on Relation between Double Laplace Transform and Double Differential Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, June.
    5. Hassan Eltayeb & Adem Kiliçman, 2013. "A Note on Double Laplace Transform and Telegraphic Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
    Full references (including those not matched with items on IDEAS)

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