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Analytic and Approximate Solutions of the Space‐Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method

Author

Listed:
  • Sara H. M. Hamed
  • Eltayeb A. Yousif
  • Arbab I. Arbab

Abstract

A combination of homotopy perturbation method and Sumudu transform is applied to find exact and approximate solution of space and time fractional nonlinear Schrödinger equation. The fractional derivatives are described in the Caputo sense. The solutions are given in the form of convergent series with easily computable components. The results show that the method is effective and convenient for solving nonlinear differential equations of fractional order.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:863015
    DOI: 10.1155/2014/863015
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    References listed on IDEAS

    as
    1. Abdon Atangana & Adem Kılıçman, 2013. "The Use of Sumudu Transform for Solving Certain Nonlinear Fractional Heat-Like Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    2. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag‐Leffler Functions and Their Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    3. 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.
    4. Fatima A. Alawad & Eltayeb A. Yousif & Arbab I. Arbab, 2013. "A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations," International Journal of Differential Equations, Hindawi, vol. 2013, pages 1-10, December.
    5. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    6. 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).
    7. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
    8. 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).
    Full references (including those not matched with items on IDEAS)

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