Applications of the Generalized Marcum Q-Function to Janowski Subclasses of Harmonic Functions

In this work, we provide a convolution type operator Λν,b that is produced by the generalized Marcum Q-function and examine how it maps to various Janowski-type subclasses of harmonic univalent functions. Since the Marcum Q-function has an integral form via the lower incomplete gamma function, the convolution operator Λν,b can be understood as a fractional type integral operator operating on the coefficients of harmonic mappings. Applying Λν,b to harmonic mappings f=h+g¯ in the unit disk D, we derive coefficient inequalities, and inclusion relations for various subclasses of harmonic and analytic univalent functions. In particular, we give sufficient conditions for Λν,b(f) to belong to Janowski-starlike families such as SH∗(F,G), KH0, and RH(F,G). Closure properties of the Janowski class under the proposed operator are also established. Numerical tables and examples confirm the inclusion results, and graphical plots illustrate how the operator reshapes the image domains for different parameter pairs (ν,b). Numerical illustrations are provided to visualize the geometric steering effect induced by the Marcum Q-function and its fractional-order damping behavior.