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Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs

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  • Sadeghi, S.
  • Jafari, H.
  • Nemati, S.

Abstract

Recently, Atangana and Baleanu have defined a new fractional derivative which has a nonlocal and non-singular kernel. It is called the Atangana–Baleanu derivative. In this paper we present a numerical technique to obtain solution of fractional differential equations containing Atangana–Baleanu derivative. For this purpose, we use the operational matrices based on Genocchi polynomials together with the collocation points which help us to reduce the problem to a system of algebraic equations. An error bound for the error of the operational matrix of the fractional derivative is introduced. Finally, some examples are given to illustrate the applicability and efficiency of the proposed method.

Suggested Citation

  • Sadeghi, S. & Jafari, H. & Nemati, S., 2020. "Operational matrix for Atangana–Baleanu derivative based on Genocchi polynomials for solving FDEs," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    • Handle: RePEc:eee:chsofr:v:135:y:2020:i:c:s0960077920301387
    DOI: 10.1016/j.chaos.2020.109736
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    References listed on IDEAS

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    1. Abu Arqub, Omar & Al-Smadi, Mohammed, 2018. "Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 161-167.
    2. Emile F. Doungmo Goufo & Ignace Tchangou Toudjeu, 2018. "Around Chaotic Disturbance and Irregularity for Higher Order Traveling Waves," Journal of Mathematics, Hindawi, vol. 2018, pages 1-11, June.
    3. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    4. Doungmo Goufo, Emile F. & Tenkam, H.M. & Khumalo, M., 2019. "A behavioral analysis of KdVB equation under the law of Mittag–Leffler function," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 139-145.
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    Cited by:

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    2. Rabbani, Mohsen & Das, Anupam & Hazarika, Bipan & Arab, Reza, 2020. "Measure of noncompactness of a new space of tempered sequences and its application on fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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