$\eta$-Ricci solitons and gradient Ricci solitons on $f$-Kenmotsu manifolds

The aim of the present research article is to discuss the $f$-Kenmotsu manifolds with respect to a semi-symmetric non-metric connection conceding an $\eta$-Ricci soliton and gradient Ricci soliton. Moreover, we prove that the second order symmetric tensor is a constant multiple of the metric tensor and parallel with respect to the semi-symmetric non-metric connection. In addition,we illustrate an example to exhibit that $3$-dimensional $f$-Kenmotsu manifolds with a semi-symmetric non-metric connection concede an expanding $\eta$-Ricci soliton. Finally, it is shown that locally $\phi$-symmetric $3$-dimensional $f$-Kenmotsu manifolds with a semi-symmetric non-metric connection concede a gradient Ricci soliton.