Fractional nonlinear electrical lattice

We examine the linear and nonlinear modes of a one-dimensional electrical lattice, where usual discrete Laplacian is replaced by fractional Laplacian. This induces long-range intersite coupling that, at long distances, decreases as power law. In regime, we compute both, spectrum plane waves mean square displacement (MSD) an initially localized excitation, in closed form terms regularized hypergeometric functions exponent. The MSD shows ballistic behavior times, MSD$\sim t^2$ for all exponents. When exponent decreased from its standard integer value, bandwidth density states tendency towards degeneracy. limit vanishing exponent, system becomes completely degenerate. For numerically low-lying modes, function A modulational stability computation decreases, number solitons generated also eventually collapsing into single soliton.