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Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative

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  • Akgül, Ali
  • Modanli, Mahmut

Abstract

In this paper, the third order partial differential equation defined by Caputo fractional derivative with Atangana–Baleanu derivative has been investigated. The stability estimates are proved for the exact solution. Difference schemes for Crank–Nicholson finite difference scheme method is constructed. The stability of difference schemes for this problem is shown by Von Neumann method (Fourier analysis method). Numerical results with respect to the exact solution confirm the accuracy and effectiveness of the technique. The reproducing kernel function for the problem has been found.

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  • Akgül, Ali & Modanli, Mahmut, 2019. "Crank–Nicholson difference method and reproducing kernel function for third order fractional differential equations in the sense of Atangana–Baleanu Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 10-16.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:10-16
    DOI: 10.1016/j.chaos.2019.06.011
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    References listed on IDEAS

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    1. 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.
    2. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    3. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    4. Allaberen Ashyralyev & Pavel E. Sobolevskii, 2005. "Two new approaches for construction of the high order of accuracy difference schemes for hyperbolic differential equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2005, pages 1-31, January.
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    Cited by:

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