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A Numerical Method to Solve Higher-Order Fractional Differential Equations

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Abstract

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

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Authors and Affiliations

  1. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Ricardo Almeida & Nuno R. O. Bastos

  2. Department of Mathematics, School of Technology and Management of Viseu, Polytechnic Institute of Viseu, 3504-510, Viseu, Portugal

    Nuno R. O. Bastos

Authors
  1. Ricardo Almeida
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  2. Nuno R. O. Bastos
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Correspondence to Ricardo Almeida.

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Almeida, R., Bastos, N.R.O. A Numerical Method to Solve Higher-Order Fractional Differential Equations. Mediterr. J. Math. 13, 1339–1352 (2016). https://doi.org/10.1007/s00009-015-0550-2

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  • DOI: https://doi.org/10.1007/s00009-015-0550-2

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