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Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus

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  • Abdon Atangana
  • Seyma Tuluce Demiray
  • Hasan Bulut

Abstract

The aim of this paper was to first extend the model describing the nonlinear wave movement to the concept of noninteger order derivative. The extended equation was investigated within the scope of an iterative method. The stability and convergence analysis of the iteration method for this extended equation was presented in detail. The uniqueness of the special solution was also investigated. A resume of the method for solving this equation was provided. The algorithm was used to derive the unique special solution for given initial conditions.

Suggested Citation

  • Abdon Atangana & Seyma Tuluce Demiray & Hasan Bulut, 2014. "Modelling the Nonlinear Wave Motion within the Scope of the Fractional Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:481657
    DOI: 10.1155/2014/481657
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    1. Carl M. Bender & Steven A. Orszag, 1999. "Advanced Mathematical Methods for Scientists and Engineers I," Springer Books, Springer, number 978-1-4757-3069-2, March.
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    Cited by:

    1. Seyma Tuluce Demiray & Yusuf Pandir & Hasan Bulut, 2014. "Generalized Kudryashov Method for Time‐Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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