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Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation

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  • Zheng, Bailin
  • Kai, Yue
  • Xu, Wenlong
  • Yang, Nan
  • Zhang, Kai
  • Thibado, P.M.

Abstract

In this study, solutions to the nonlinear time-dependent fractional reaction–diffusion equation with conformal fractional derivative is considered. In the first part of the manuscript, we reduce the fractional equation to a traditional differential equation using the fractional complex transformation. Two cases where the exact solution exists are then presented. One of these solutions is used to model experimental data showing anomalous diffusion in freestanding graphene. In the second part, we study the traveling solutions and present two cases: Canonical-like transformation method and complete discrimination system for polynomial method.

Suggested Citation

  • Zheng, Bailin & Kai, Yue & Xu, Wenlong & Yang, Nan & Zhang, Kai & Thibado, P.M., 2019. "Exact traveling and non-traveling wave solutions of the time fractional reaction–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310349
    DOI: 10.1016/j.physa.2019.121780
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    Citations

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    Cited by:

    1. Rizvi, Syed T.R. & Seadawy, Aly R. & Ahmed, Sarfaraz & Younis, Muhammad & Ali, Kashif, 2021. "Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Lewa’ Alzaleq & Valipuram Manoranjan, 2023. "Analysis of a Reaction–Diffusion–Advection Model with Various Allee Effects," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    3. Owolabi, Kolade M. & Jain, Sonal, 2023. "Spatial patterns through diffusion-driven instability in modified predator–prey models with chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Qi, Jianming & Cui, Qinghua & Bai, Leiqiang & Sun, Yiqun, 2024. "Investigating exact solutions, sensitivity, and chaotic behavior of multi-fractional order stochastic Davey–Sewartson equations for hydrodynamics research applications," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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