Research Article Open Access

An Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series Scheme

Radwan Abu-Gdairi1, Mohammed Al-Smadi2 and Ghaleb Gumah2
  • 1 Zarqa Private University, Jordan
  • 2 Al-Balqa Applied University, Jordan

Abstract

In this study, we present a new analytical numerical technique for solving a class of time Fractional Differential Equations (FDEs) with variable coefficients based on the generalized Taylor series formula in the Caputo sense. This method provided the solution in the form of a rapidly convergent power series under a multiple fractional differentiability with easily computable components. An efficacious experiment is given to guarantee the procedure, to illustrate the theoretical statements of the present technique and to show its potentiality, generality and superiority for solving wide range of FDEs. The results reveal that the method is easy to implement, very effective, fully compatible with the complexity of such problems, straightforward and simple.

Journal of Mathematics and Statistics
Volume 11 No. 2, 2015, 29-38

DOI: https://doi.org/10.3844/jmssp.2015.29.38

Submitted On: 16 July 2015 Published On: 18 September 2015

How to Cite: Abu-Gdairi, R., Al-Smadi, M. & Gumah, G. (2015). An Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series Scheme. Journal of Mathematics and Statistics, 11(2), 29-38. https://doi.org/10.3844/jmssp.2015.29.38

  • 3,169 Views
  • 1,909 Downloads
  • 16 Citations

Download

Keywords

  • Fractional Differential Equation
  • Residual Power Series Method
  • Approximate Solution
  • Series Expansion Representation