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An Efficient Series Solution for Fractional Differential Equations

Author

Listed:
  • Mohammed Al-Refai
  • Mohamed Ali Hajji
  • Muhammad I. Syam

Abstract

We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo′s type. The new approach is a modified form of the well‐known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.

Suggested Citation

  • Mohammed Al-Refai & Mohamed Ali Hajji & Muhammad I. Syam, 2014. "An Efficient Series Solution for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:891837
    DOI: 10.1155/2014/891837
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    References listed on IDEAS

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    1. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, January.
    2. Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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