A Legendre spectral finite difference method for the solution of non-linear space-time fractional Burger’s–Huxley and reaction-diffusion equation with Atangana–Baleanu derivative
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DOI: 10.1016/j.chaos.2019.109402
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- Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
- 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.
- Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Taneco-Hernández, M.A., 2018. "Fractional conformable derivatives of Liouville–Caputo type with low-fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 424-438.
- 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.
- Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
- 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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Cited by:
- Faheem, Mo & Khan, Arshad & Raza, Akmal, 2022. "A high resolution Hermite wavelet technique for solving space–time-fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 588-609.
- Cao, Baiheng & Wu, Xuedong & Wang, Yaonan & Zhu, Zhiyu, 2024. "Modified hybrid B-spline estimation based on spatial regulator tensor network for burger equation with nonlinear fractional calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 253-275.
- Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2020. "Application of fractional Gegenbauer functions in variable-order fractional delay-type equations with non-singular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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Keywords
Fractional PDE; Diffusion equation; Atangana–Baleanu fractional derivative; Burger’s–Huxley equation; Legendre polynomial; Spectral method; Finite difference method;All these keywords.
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