The study of blood flow in cylindrical geometries resembling small arteries is crucial for advancing drug delivery systems, cardiovascular health, and treatment methods. However, Conventional models have failed to capture the complex memory effects and non-local behavior inherent in blood flow dynamics, which hinders their accuracy in predicting critical flow and heat transfer properties for medical applications. To overcome these limitations, this research introduces a novel fractional-order magnetohydrodynamic model for blood flow, incorporating a ZnO and Fe3O4 hybrid nanofluid. The model uniquely integrates boundary slip velocity effects within the double fractional Maxwell model (DFMM) rheology framework and utilizes the dual fractional phase lag bioheat model (DFPLM) applied to a porous cylindrical structure. Fractional-order time derivatives in the thermal and momentum equations are formulated using the Caputo approach, with numerical solutions derived via finite difference methods leveraging L1 and L2 approximations for Caputo fractional derivatives. The study examines the effects of fractional orders, relaxation time, and phase lags for heat and temperature, along with parameters such as thermal radiation, wall slip velocity, and porosity. These factors are analyzed for their impact on velocity, temperature, skin friction, and the Nusselt number. Results indicate that the hybrid nanofluid enhances heat transfer compared to blood or mono-hybrid nanofluids, while also reducing skin friction. Furthermore, fractional-order models provide more reliable and realistic predictions under varying flow conditions. The DFMM shows smoother transitions in velocity and friction, while the DFPLM predicts higher temperatures and greater heat transfer enhancement compared to classical and single-phase lag models. By integrating fractional calculus, this model offers improved simulation of complex transport phenomena in small arteries, contributing to the development of more effective cardiovascular treatments.