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Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Author

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  • Adel Al-Rabtah
  • Shaher Momani
  • Mohamed A. Ramadan

Abstract

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for 0 < α ≤ 1 and α ≥ 1 , where α denotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

Suggested Citation

  • Adel Al-Rabtah & Shaher Momani & Mohamed A. Ramadan, 2012. "Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, March.
    • Handle: RePEc:hin:jnlaaa:426514
    DOI: 10.1155/2012/426514
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    Cited by:

    1. Nur Amirah Zabidi & Zanariah Abdul Majid & Adem Kilicman & Faranak Rabiei, 2020. "Numerical Solutions of Fractional Differential Equations by Using Fractional Explicit Adams Method," Mathematics, MDPI, vol. 8(10), pages 1-23, October.

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