Abstract
In this paper, we consider a class of nonlinear damped dynamic equations on time scales within conformable fractional derivative. We accommodate the newly defined conformable time-scale fractional calculus to establish new oscillation criteria for the solutions of canonical and noncanonical form of the proposed equation. Our approach is based on the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus and certain mathematical inequalities. Applications of the established results demonstrate that one can obtain oscillation criteria for both fractional differential equations and fractional difference equations simultaneously. The validity of the main results are also illustrated by some examples.