Equivalent Frechet differentiable norm on $\ell_1$ and $c_0$

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Does there exist an equivalent Frechet differentiable norm on $\ell_1$ and $c_0$? I think we can not find an equivalent norm on $\ell_1$ but we could find an equivalent norm on $c_0$, I do not prove this claim, only I guess it is true, please help me. thanks