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An efficient cubic spline approximation for variable-order fractional differential equations with time delay

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Abstract

This paper describes a robust, accurate and efficient scheme based on a cubic spline interpolation. The proposed scheme is applied to approximate variable-order fractional integrals and is extended to solve a class of nonlinear variable-order fractional equations with delay. Modified Hutchinson equation and delay Ikeda equation are solved using the proposed scheme. The efficiency and accuracy of the proposed method are analyzed in the perspective of the mean absolute error and experimental convergence order. Numerical results confirm the accuracy and efficiency of the proposed scheme.

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Authors and Affiliations

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

    Shole Yaghoobi & Behrouz Parsa Moghaddam

  2. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Karim Ivaz

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  1. Shole Yaghoobi
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Correspondence to Behrouz Parsa Moghaddam.

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Yaghoobi, S., Moghaddam, B.P. & Ivaz, K. An efficient cubic spline approximation for variable-order fractional differential equations with time delay. Nonlinear Dyn 87, 815–826 (2017). https://doi.org/10.1007/s11071-016-3079-4

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