Coefficient estimates and distortion bounds for rabotnov functions with application to digital image warping

This study introduces and investigates new subclasses of univalent functions in the open unit disk, defined through the convolution of normalized analytic functions with a generalized Rabotnov function Rτ,δ(ζ). The main objective is to define new subclasses Rτ,δϱ,λ, Rτ,δϱ,b,λ, Rτ,δμ,λ and Rτ,δμ,b,λ, which are associated with the normalized form of the Rabotnov fractional exponential function, and to investigate their geometrical characteristics. This study obtains sharp coefficient bounds, along with growth and distortion properties belonging to these subclasses. Furthermore, radii of starlikeness, radii of convexity, and extremal functions are determined. Finally, we highlight the utility of these results in signal processing and image reconstruction. These results enhance the broader understanding of defined subclasses within geometric function theory and provide a mathematical foundation in fractional calculus, conformal mapping, and applied engineering contexts.