The target of this manuscript is to introduce new symmetric fractional $\alpha$- $\beta$- $\eta$- $\mathrm{{\rm Y}}$-contractions and prove some new fixed point results for such contractions in the setting of $M_b$-metric space. Moreover, we derive some results for said contractions on closed ball of mentioned space. The existence of the solution to a fractional-order differential equation with one boundary stipulation will be discussed.