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Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices

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  • Mohsen Alipour
  • Dumitru Baleanu

Abstract

We present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann‐Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann‐Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.

Suggested Citation

  • Mohsen Alipour & Dumitru Baleanu, 2013. "Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by BPs Operational Matrices," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:954015
    DOI: 10.1155/2013/954015
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    References listed on IDEAS

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    1. Gao, Xin & Yu, Juebang, 2005. "Synchronization of two coupled fractional-order chaotic oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 141-145.
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    3. Lu, Jun Guo, 2005. "Chaotic dynamics and synchronization of fractional-order Arneodo’s systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1125-1133.
    4. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
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    Cited by:

    1. Al-Mdallal, Qasem M., 2018. "On fractional-Legendre spectral Galerkin method for fractional Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 261-267.

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