Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger equations by using the Hirota bilinear method. In particular, abundant wave solutions of two- and three-component nonlocal nonlinear Schrödinger equations, including periodic and mixed-wave solutions, are obtained by taking appropriate values for the involved parameters in the general solution formula. Moreover, diverse wave structures of the resulting breather and periodic wave solutions with different parameters are discussed in detail.

In this paper, the fractional Benjamin–Ono differential equation with a Riemann–Liouville fractional derivative is considered using the Lie symmetry analysis method. Two symmetries admitted by the equation are obtained. Then, the equation is reduced to a fractional ordinary differential equation with an Erdélyi–Kober fractional derivative by one of the symmetries. Finally, conservation laws for the equations are constructed using the new conservation theorem.