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Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications

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Abstract

This paper proposes accurate and robust algorithms for approximating variable order fractional derivatives of arbitrary order. The proposed schemes are based on finite difference approximations. We compare the performance of algorithms by introducing a new formulation of experimental convergence order. Two initial value problems are considered and solved by means of the proposed methods. Numerical results are provided justifying the usefulness of the proposed methods.

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Authors and Affiliations

  1. Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    Behrouz Parsa Moghaddam

  2. Department of Electrical Engineering, Institute of Engineering, Rua Dr. António Bernardino de Almeida, 431, 4249-015, Porto, Portugal

    José António Tenreiro Machado

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  1. Behrouz Parsa Moghaddam
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  2. José António Tenreiro Machado
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Correspondence to Behrouz Parsa Moghaddam.

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Moghaddam, B.P., Machado, J.A.T. Extended Algorithms for Approximating Variable Order Fractional Derivatives with Applications. J Sci Comput 71, 1351–1374 (2017). https://doi.org/10.1007/s10915-016-0343-1

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  • DOI: https://doi.org/10.1007/s10915-016-0343-1

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