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Computational algorithms for computing the fractional derivatives of functions

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  • Odibat, Zaid M.

Abstract

In this paper, we propose algorithms to compute the fractional derivatives of a function by a weighted sum of function values at specified points. The fractional derivatives are considered in the Caputo sense. The error analysis of the algorithms and some illustrative examples are presented. The numerical results confirm that the new algorithms are accurate, efficient and readily implemented.

Suggested Citation

  • Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:7:p:2013-2020
    DOI: 10.1016/j.matcom.2008.08.003
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    References listed on IDEAS

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    1. Momani, Shaher, 2006. "Non-perturbative analytical solutions of the space- and time-fractional Burgers equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 930-937.
    2. 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. Jahanshahi, S. & Babolian, E. & Torres, D.F.M. & Vahidi, A.R., 2017. "A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 295-304.
    2. Md. Habibur Rahman & Muhammad I. Bhatti & Nicholas Dimakis, 2023. "Employing a Fractional Basis Set to Solve Nonlinear Multidimensional Fractional Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    3. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.

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