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A Numerical approach of fractional advection-diffusion equation with Atangana–Baleanu derivative

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  • Tajadodi, H.

Abstract

In the current paper, a new approach is applied to solve time fractional advection-diffusion equation. The utilized fractional derivative operator is the Atangana–Baleanu (AB) derivative in Caputo sense. The mentioned fractional derivative involves the Mittag–Leffler function as the kernel that is both non-singular and non-local. A new operational matrix of AB fractional integration is obtained for the Bernstein polynomials (Bps). By applying the aforesaid matrix, the considered problems are reduced to a system of equations. The approximate solution is derived by solving the yielded system. Also, the error bound is studied. The obtained results show that the applied scheme is simple and powerful tool in finding numerical solutions of fractional equations.

Suggested Citation

  • Tajadodi, H., 2020. "A Numerical approach of fractional advection-diffusion equation with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919304783
    DOI: 10.1016/j.chaos.2019.109527
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    References listed on IDEAS

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    1. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
    2. Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    3. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Computational study of multi-species fractional reaction-diffusion system with ABC operator," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 280-289.
    4. Heydari, M.H. & Atangana, A., 2019. "A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 339-348.
    5. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
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