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Nonexistence results for a fractional problem arising in thermal diffusion in fractal media

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  • Tatar, Nasser-eddine

Abstract

We consider the Cauchy problem for the fractional differential equationD1+αu+Dβu=Δu+h(t,x)|u|pwith given initial data and where p>1, −1<α<1, 0<β<2 and β<1+α. Nonexistence results and necessary conditions for global existence are established by means of the test-function method. These results improve and extend previous works.

Suggested Citation

  • Tatar, Nasser-eddine, 2008. "Nonexistence results for a fractional problem arising in thermal diffusion in fractal media," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1205-1214.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1205-1214
    DOI: 10.1016/j.chaos.2006.08.001
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    Cited by:

    1. Amal Alshabanat & Eman Almoalim & Mohamed Jleli & Bessem Samet, 2023. "A Time-Fractional Parabolic Inequality on a Bounded Interval," Mathematics, MDPI, vol. 11(24), pages 1-10, December.
    2. Tatar, Nasser-eddine, 2021. "Mittag–Leffler stability for a fractional Euler–Bernoulli problem," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).

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