Universal damping and phase shifts in neutrino oscillations from fractional action measures

We investigate the consequences of using a fractional action-like variational principle without introducing fractional derivatives, but instead incorporating a nonlocal fractional weight in the spacetime measure. The weight is taken in the Riemann–Liouville–type form [Formula: see text]/ [Formula: see text] where x[Formula: see text] are the spacetime variables, are fixed reference parameters, and [Formula: see text] is a fractional parameter. Starting from this weighted action, we derive the modified Klein–Gordon and Dirac equations and show that the resulting dynamics differs from the standard relativistic field equations by additional first-order derivative terms proportional to gradients of the logarithm of the weight. These terms render the theory explicitly nonconservative and lead to non-Hermitian effective Hamiltonians, while preserving a conserved weighted current. We study in detail the structure of the Dirac equation, its Hamiltonian form, charge-conjugation properties, and chiral decomposition, emphasizing the physical impact on antimatter dynamics and neutrino propagation. Charge conjugation symmetry is preserved, while parity and time reversal may be broken depending on the functional form of the weight, and CPT is not guaranteed due to explicit Lorentz-violation and modified Hermiticity assumptions. In the ultra-relativistic limit relevant for neutrinos, we derive an effective Schrödinger-like evolution equation for flavor amplitudes, showing that the fractional weight induces a universal damping factor multiplying standard oscillation probabilities and, in more general cases, potential MSW-like phase shifts. We discuss phenomenological implications and constraints from neutrino experiments and clarify the conditions under which observable deviations from standard quantum field theory may arise.