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The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat‐Like Equations

Author

Listed:
  • Abdon Atangana
  • Adem Kılıçman

Abstract

We make use of the properties of the Sumudu transform to solve nonlinear fractional partial differential equations describing heat‐like equation with variable coefficients. The method, namely, homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the HPM using He’s polynomials. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional differential equations arising in different fields of science and engineering.

Suggested Citation

  • Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat‐Like Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:737481
    DOI: 10.1155/2013/737481
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    References listed on IDEAS

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    1. Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, February.
    2. Adem Kiliçman & Hassan Eltayeb & Ravi P. Agarwal, 2010. "On Sumudu Transform and System of Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Adem Kiliçman & Hassan Eltayeb & Ravi P. Agarwal, 2010. "On Sumudu Transform and System of Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-11, April.
    4. Jagdev Singh & Devendra Kumar & A. Kılıçman, 2013. "Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Sara H. M. Hamed & Eltayeb A. Yousif & Arbab I. Arbab, 2014. "Analytic and Approximate Solutions of the Space‐Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Abdon Atangana & Suares Clovis Oukouomi Noutchie, 2014. "Novel Approach for Dealing with Partial Differential Equations with Mixed Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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