Novel series representation of degenerate gamma function with formulation of new generalized kinetic equation

The degenerate gamma function is a recently developed special function associated with the classical beta function. This study employs the complex delta function to investigate a novel series representation of the degenerate gamma function. While this family of functions has been the focus of considerable academic interest, the fractional kinetic equation has remained unexplored due to the presence of an infinite number of singularities at ($z = - n;$z=−n; $z = n + {1 \over {\rm{\lambda }}};n = 0,1,2, \ldots $z=n+1λ;n=0,1,2,…) This work solves the fractional kinetic equation involving the degenerate gamma function and derives new fractional transform equations by introducing a new representation. Various generalized properties of the degenerate gamma function are analysed using the Fourier transform. The results are validated with the classical identities, and specific cases involving the classical beta and gamma functions are provided as corollaries. One cannot explore the degenerate gamma function in this way using its existing representations.