This paper develops a deformed theory of harmonic univalent mappings by introducing the class \(S_H^{0;(q,\tau)}\) , obtained by applying a (q,τ)-fractional operator to functions in the classical harmonic class \(S_H^0(S)\) of Ponnusamy and Sairam Kaliraj. The construction incorporates the shearing method for generating harmonic mappings convex in a prescribed direction, together with a (q,τ)-Caputo-type deformation acting on the analytic and co-analytic parts. This produces a family of harmonic mappings whose growth, curvature, and distortion properties depend explicitly on the deformation parameters \(q\in(0,1)\) and \(\tau\ge0\) . We establish analytic and coefficient criteria guaranteeing that \(F^{(q,\tau)}=H+\overline{G}\) is harmonic, sense-preserving, and univalent, including a Starkov-type condition adapted to the (q,τ)-setting. The (q,τ)-order \(\alpha_{q,\tau}\) of the class is defined and shown to exist, providing a quantitative measure of the geometric strength of the deformation. Several consequences are derived, including coefficient bounds, stable harmonic univalence under \((q,\tau,\alpha)\) -fractional shears, and explicit criteria for deformed Koebe-type mappings. The results demonstrate that the parameters q and τ interpolate smoothly between the classical harmonic theory and a new family of fractionally deformed harmonic mappings with enriched geometric structure. Finally, we demonstrate that the \((q,\tau,\alpha)\) -harmonic deformation enhances edge detection in digital images.
