Geodesic
Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group
Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 01-14.

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Denoting by Dα0|t the time-fractional derivative of order α (α ∈ (0, 1)) in the sense of Caputo, and by ∆H the Laplacian operator on the (2N + 1) - dimensional Heisenberg group H^N, we prove some nonexistence results for solutions to problems of the type Dα0|tu − ∆H(au) >= |u|^p, Dα0|tu − ∆H(au) >= |v|^p, Dδ0|tv − ∆H(bv) >= |u|^q, in H^N × R+ , with a, b ∈ L ∞ (H^N × R+). For α = 1 (and δ = 1 in the case of two inequalities), we retrieve the results obtained by Pohozaev-Véron [10] and El Hamidi-Kirane [3] corresponding, respectively, to the parabolic inequalities and parabolic system.
Keywords: Fractional Derivatives, Heisenberg Group, Semilinear Differential Inequalities, 26A33, 33C60, 44A15, 35K55 
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Haouam, K.; Sfaxi, M. Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group. Fractional calculus and applied analysis, Tome 12 (2009) no. 1, pp. 01-14. http://geodesic.mathdoc.fr/item/FCAA_2009_12_1_a0/