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A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets

Author

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  • Aydin Secer

    (Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey)

  • Selvi Altun

    (Yildiz Technical University, Istanbul 34200, Turkey)

Abstract

This paper introduces a new numerical approach to solving a system of fractional differential equations (FDEs) using the Legendre wavelet operational matrix method (LWOMM). We first formulated the operational matrix of fractional derivatives in some special conditions using some notable characteristics of Legendre wavelets and shifted Legendre polynomials. Then, the system of fractional differential equations was transformed into a system of algebraic equations by using these operational matrices. At the end of this paper, several examples are presented to illustrate the effectivity and correctness of the proposed approach. Comparing the methodology with several recognized methods demonstrates that the advantages of the Legendre wavelet operational matrix method are its accuracy and the understandability of the calculations.

Suggested Citation

  • Aydin Secer & Selvi Altun, 2018. "A New Operational Matrix of Fractional Derivatives to Solve Systems of Fractional Differential Equations via Legendre Wavelets," Mathematics, MDPI, vol. 6(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:11:p:238-:d:180701
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    References listed on IDEAS

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    1. Constantin Bota & Bogdan Căruntu, 2015. "Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-5, March.
    2. F. Mohammadi & M.M. Hosseini & Syed Tauseef Mohyud-Din, 2011. "Legendre wavelet Galerkin method for solving ordinary differential equations with non-analytic solution," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(4), pages 579-585.
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