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An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order

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Abstract

This paper proposes an cost-efficient method for the numerical solution of fractional differential equations of multi-order. The suggested algorithm adopts the operational matrix of fractional derivative in term of Caputo sense using modified cubic B-spline functions. The new method leads to a system of algebraic equations that improves the solution accuracy and reduces the computational complexity. Several numerical examples illustrate the applicability of the proposed method.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Malayer University, P. O. Box 16846-13114, Malayer, Iran

    K. Sayevand

  2. Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Porto, Portugal

    J. Tenreiro Machado

Authors
  1. K. Sayevand
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  2. J. Tenreiro Machado
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Correspondence to K. Sayevand.

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Communicated by Vasily E. Tarasov.

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Sayevand, K., Machado, J.T. An accurate and cost-efficient numerical approach to analyze the initial and boundary value problems of fractional multi-order . Comp. Appl. Math. 37, 6582–6600 (2018). https://doi.org/10.1007/s40314-018-0700-9

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  • DOI: https://doi.org/10.1007/s40314-018-0700-9

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