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Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration

Author

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  • İbrahim Avcı

    (Department of Mathematics, Eastern Mediterranean University, Famagusta, TR 99628, Northern Cyprus, via Mersin-10, Turkey)

  • Nazim I. Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, Famagusta, TR 99628, Northern Cyprus, via Mersin-10, Turkey)

Abstract

In this article, we propose a numerical method based on the fractional Taylor vector for solving multi-term fractional differential equations. The main idea of this method is to reduce the given problems to a set of algebraic equations by utilizing the fractional Taylor operational matrix of fractional integration. This system of equations can be solved efficiently. Some numerical examples are given to demonstrate the accuracy and applicability. The results show that the presented method is efficient and applicable.

Suggested Citation

  • İbrahim Avcı & Nazim I. Mahmudov, 2020. "Numerical Solutions for Multi-Term Fractional Order Differential Equations with Fractional Taylor Operational Matrix of Fractional Integration," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:96-:d:306049
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    References listed on IDEAS

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    3. Pundikala Veeresha & Doddabhadrappla Gowda Prakasha & Dumitru Baleanu, 2019. "An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation," Mathematics, MDPI, vol. 7(3), pages 1-18, March.
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    5. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    6. Jianping Liu & Xia Li & Limeng Wu, 2016. "An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, June.
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    Cited by:

    1. Etemad, Sina & Avci, Ibrahim & Kumar, Pushpendra & Baleanu, Dumitru & Rezapour, Shahram, 2022. "Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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