Fractional Quantum Models and the Properties of Hadrons

The study of heavy quarkonia (charm, bottom) alongside heavy-light mesons (D, B) and baryons (¿ c¿ ,¿ cc¿ ) is essential for mapping Quantum Chromodynamics (QCD) within its non-perturbative, confining regime. While traditional relativistic and non-relativistic wave equations provide a baseline, augmenting them with fractional calculus offers a robust mathematical framework. This approach effectively captures the anomalous diffusion and long-range structural interactions inherent to QCD color confinement.1. Non-Relativistic Systems: The Fractional Schrödinger Equation For heavy-heavy systems (quarkonia), where the large reduced mass justifies a non-relativistic approach, the N-radial generalized fractional Schrödinger equation (SE) is applied. Mechanism: The standard kinetic energy operator is replaced by a fractional derivative of order ¿ (where 0