On a Fully Unified k-Space Extension of Ramanujan's Master Theorem with Applications to Fractional Special Functions

We introduce a fully symmetric, native k-space generaliza-tion of Ramanujan’s Master Theorem (RMTk). Prior hybrid approachesinside the literature often utilize classical Mellin kernels or standardfactorial denominators to extend the structural features of the theo-rem. In contrast, this paper establishes a unified operator ecosystemby pairing a dedicated k-Mellin integral operator with an alternatingseries expansion scaled purely by the k-Gamma function (Γk(nk + k)).Furthermore, we establish the analytical validity of this framework byformulating modified, parameter-dependent k-Hardy growth conditionson the complex plane. Finally, we showcase the operational efficiencyof our theorem by deriving a novel, closed-form solution for a semi-infinite integral containing a two-parameter k-Mittag-Leffler kernel.