Short communicationPersistence of nonlinear hysteresis in fractional models of Josephson transmission lines

- A space-fractional array that generalizes the Josephson transmission model is proposed.
- Simulations show that nonlinear supratransmission and infratransmission are present in the fractional array.
- Nonlinear hysteresis cycles are calculated for various values of the fractional derivative order.
- An application of the nonlinear bistability of the system is proposed.

In this note, we depart from a model describing the transmission of electric currents in Josephson-junction chains, and provide a fractional generalization using Riesz discrete differential operators. The fractional model considered has generalized Hamiltonian- and energy-like functionals. The model and the energy functionals are fully discretized in order to investigate numerically the complex dynamics of the system when a sinusoidal perturbation at one end of the chain is imposed. As one of the most important results in this report, we establish the persistence of the nonlinear phenomena of supratransmission and infratransmission in Riesz fractional chains. Nonlinear hysteresis loops are obtained numerically for some values of the order of the fractional derivative, and numerical simulations of the propagation of monochromatic wave signals through the transmission line are presented using the nonlinear bistability of the system.