Structural limitations of non-singular fractional operators with bounded memory

Fractional operators with bounded, non-singular memory are often presented as introducing new dissipative mechanisms. This work proves the opposite. Under minimal structural axioms (causality, bounded memory, passivity, non-oscillatory relaxation), any admissible operator necessarily reduces to a superposition of purely relaxing modes. No oscillatory, resonant, or energy-storing memory is compatible with these constraints. In particular, bounded-memory fractional modifications of Navier–Stokes equations cannot generate genuinely new dissipative dynamics.