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Operational Matrix of Fractional Integration Based on the Shifted Second Kind Chebyshev Polynomials for Solving Fractional Differential Equations

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Abstract

This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M −κ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Narmak, P.O. Box 16846, 13114, Tehran, Iran

    Khosrow Maleknejad

  2. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box 35195-363, Semnan, Iran

    Kazem Nouri & Leila Torkzadeh

Authors
  1. Khosrow Maleknejad
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  2. Kazem Nouri
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  3. Leila Torkzadeh
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Correspondence to Kazem Nouri.

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Maleknejad, K., Nouri, K. & Torkzadeh, L. Operational Matrix of Fractional Integration Based on the Shifted Second Kind Chebyshev Polynomials for Solving Fractional Differential Equations. Mediterr. J. Math. 13, 1377–1390 (2016). https://doi.org/10.1007/s00009-015-0563-x

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  • DOI: https://doi.org/10.1007/s00009-015-0563-x

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