Applications of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si164.svg" display="inline" id="d1e117"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:

The ( q , τ ) -Gamma function provides a two-parameter extension of the classical and q -deformed Gamma functions, enabling enhanced modeling of memory and scaling effects in fractional calculus and special functions. This paper presents the definition, key properties, and computational aspects of the ( q , τ ) -Gamma function Applications in generalized fractional derivatives, integral transforms, and ( q , τ ) -special polynomials are described, with selected examples and discussion of future directions.