Research Article Open Access

Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method

Eman Abuteen1, Asad Freihat1, Mohammed Al-Smadi1, Hammad Khalil2 and Rahmat Ali Khan2
  • 1 Al-Balqa Applied University, Jordan
  • 2 University of Malakand, Pakistan

Abstract

This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different values of fractional-order α is shown graphically. A comparative study is presented between the FRDTM and Implicit Runge-Kutta approach to illustrate the efficiency and reliability of the proposed technique. Our numerical investigations indicate that the FRDTM is simple, powerful mathematical tool and fully compatible with the complexity of such problems.

Journal of Mathematics and Statistics
Volume 12 No. 1, 2016, 23-33

DOI: https://doi.org/10.3844/jmssp.2016.23.33

Submitted On: 17 October 2015 Published On: 26 March 2016

How to Cite: Abuteen, E., Freihat, A., Al-Smadi, M., Khalil, H. & Khan, R. A. (2016). Approximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform Method. Journal of Mathematics and Statistics, 12(1), 23-33. https://doi.org/10.3844/jmssp.2016.23.33

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Keywords

  • Nonlinear Partial Differential Equation
  • Fractional Calculus
  • Series Solution
  • Fractional Reduced Differential Transform Method
  • Caputo Time-Fractional Derivative