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Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative

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  • Kumar, Sachin
  • Pandey, Prashant

Abstract

In this presented paper, we investigate the novel numerical scheme for the non-linear reaction-diffusion equation and non-linear integro reaction-diffusion equation equipped with Atangana Baleanu derivative in Caputo sense (ABC). A difference scheme with the help of Taylor series is applied to deal with fractional differential term in the time direction of differential equation. We applied a numerical method based on quasi wavelet for discretization of unknown function and their spatial derivatives. A formulation to deal with Dirichlet boundary condition is also included. To demonstrate the effectiveness and validity of our proposed method some numerical examples are also presented. We compare our obtained numerical results with the analytical results and we conclude that quasi wavelet method achieve accurate results and this method has a distinctive local property. On the other hand the method is easy to apply on higher order fractional partial differential equation and integro differential equation.

Suggested Citation

  • Kumar, Sachin & Pandey, Prashant, 2020. "Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919304023
    DOI: 10.1016/j.chaos.2019.109456
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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. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    3. Atangana, Abdon & Khan, Muhammad Altaf, 2019. "Validity of fractal derivative to capturing chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 50-59.
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    2. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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