An iterative programmable framework to decouple time fractional responses in Stokes-type boundary layer flows

This study proposes a unified analytical methodology for systematically solving and interpreting k-linearly coupled diffusion-reaction fractional systems arising in Stokes-type boundary-layer flows past infinite surfaces. The proposed solution representation expresses each boundary-layer response as a superposition of physically interpretable partial solutions, each associated with a distinct pathway through which boundary forcing propagates across the coupled system. A Response Decomposition-Based (RDB) analysis is developed to quantify these instantaneous mechanism-specific contributions, enabling for the first time, quantitative attribution of amplification, suppression, and dominance within such memory-dependent systems. All fractional-model-specific complexity is confined to a single step, providing an efficient unified solution framework that can be reused across fractional models. To demonstrate generality and applicability, explicit analytical solutions are derived under power-law wall forcing for classical, Caputo, Caputo-Fabrizio, and Atangana-Baleanu fractional heat and mass transfer models. The analysis reveals that fractional models exhibit early-time dominance of suppressive mechanisms due to non-local memory effects, followed by a temporal crossover relative to classical responses. An inverse relationship between contribution and dominance is observed for single-path driven enhancive and suppressive boundary layer mechanisms, indicating that dominance may also arise from reduced opposition rather than strong forcing.The framework further admits structured extensions to heterogeneous-memory systems and is directly applicable to time-fractional hybrid nanofluid boundary-layer flows, enabling mechanism-specific optimization of coupled transport processes. Although presently limited to linearly coupled systems and specific parameter regimes, the methodology provides a scalable foundation for analytical decoupling, rigorous mechanism attribution, and optimization in fractional derivative based boundary-layer flows.