Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

In this paper, we prove the fractional logarithmic Sobolev inequality on homogeneous groups. Also, we establish fractional logarithmic Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups. In addition, we show blow-up results for the fractional heat equation with logarithmic nonlinearity on homogeneous groups