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On a time fractional reaction diffusion equation

Author

Listed:
  • Ahmad, B.
  • Alhothuali, M.S.
  • Alsulami, H.H.
  • Kirane, M.
  • Timoshin, S.

Abstract

A reaction diffusion equation with a Caputo fractional derivative in time and with various boundary conditions is considered. Under some conditions on the initial data, we show that solutions may experience blow-up in a finite time. However, for realistic initial conditions, solutions are global in time. Moreover, the asymptotic behavior of bounded solutions will be analyzed.

Suggested Citation

  • Ahmad, B. & Alhothuali, M.S. & Alsulami, H.H. & Kirane, M. & Timoshin, S., 2015. "On a time fractional reaction diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 199-204.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:199-204
    DOI: 10.1016/j.amc.2014.06.099
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    Cited by:

    1. Belmahi, Naziha & Shawagfeh, Nabil, 2021. "A new mathematical model for the glycolysis phenomenon involving Caputo fractional derivative: Well posedness, stability and bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Chen, Xuehui & Zhu, Hongli & Zhang, Xinru & Zhao, Lutao, 2022. "A novel time-varying FIGARCH model for improving volatility predictions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    3. Lenzi, E.K. & Menechini Neto, R. & Tateishi, A.A. & Lenzi, M.K. & Ribeiro, H.V., 2016. "Fractional diffusion equations coupled by reaction terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 9-16.

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