Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions is defined using a generalized differential operator and we have discussed a subclass \(TS_{\sigma, \delta} ^{~ \wp} (\vartheta ,\hbar ,\ell )\) of univalent functions with negative coefficients related to differential operator in the unit disk \( \mathbb { U }=\left \{{z \in \mathbb{ C }:|z|<1}\right \}\). We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class.