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In this work we deal with the local in time propagation of chaos withoutcut-off for some two dimensional fractional Keller Segel equations. Moreprecisely the diffusion considered here is given by the fractional Laplacianoperator $-(-\Delta)^{\frac{a}{2}}$ with $a \in (1,2)$ and the singularity ofthe interaction is of order $|x|^{1-\alpha}$ with $\alpha\in ]1,a]$. In thecase $\alpha\in (1,a)$ we give a complete propagation of chaos result, provingthe $\Gamma$-l.s.c property of the fractional Fisher information, already knownfor the classical Fisher information, using a result of Mischler and Hauray. Inthe fair competition case $a=\alpha$, we only prove a convergence/consistencyresult in a sub-critical mass regime, similarly as the result obtained for theclassical Keller-Segel equation.

Propagation of chaos for some 2 dimensional fractional Keller Segel equations in diffusion dominated and fair competition cases