Chiral Solitons With Fractional Temporal Evolution in Quantum Hall Effect

This study investigates the chiral nonlinear Schrödinger equation for current-dependent nonlinear wave propagation in the fractional quantum Hall setting when temporal evolution is represented by the conformable fractional derivative. This derivative is defined operationally as the ordinary first time derivative multiplied by a time-dependent power factor determined by the fractional order. The physical objective is to clarify how fractionally rescaled temporal evolution modifies coherent chiral excitations associated with quantum Hall edge-state dynamics. The novelty lies in a unified quartic auxiliary-equation classification based on the modified sub–ODE method rather than the derivation of isolated wave forms. A conformable traveling-wave reduction produces an amplitude problem whose admissible branches yield localized solitary waves, kink-type waves, singular structures, Jacobi elliptic waves, Weierstrass elliptic waves, and mixed solution families with explicit existence restrictions. The results are validated by direct substitution into the reduced and original models, together with first-integral and limiting-case checks. The analysis shows that, for fixed reduced coefficients, the fractional order changes the temporal scaling, phase evolution, and propagation trajectory while preserving the analytical amplitude family. This separation provides a useful mechanism for tuning the phase and propagation of chiral wave structures without altering their intrinsic analytical profile.