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In this paper, we utilize Fokas method to investigate the initial-boundaryvalue problems (IBVPs) of the fourth-order dispersive nonlinear Schr\"{o}dinger(FODNLS) equation on the half-line, which can simulate the nonlineartransmission and interaction of ultrashort pulses in the high-speed opticalfiber transmission system, and describe the nonlinear spin excitationphenomenon of one-dimensional Heisenberg ferromagnetic chain with eight polesand dipole interaction. By discussing the eigenfunctions of Lax pair of FODNLSequation and the analysis and symmetry of the scattering matrix, the IBVPs ofFODNLS equation is expressed as a matrix Riemann-Hilbert (RH) problem form.Then one can get the potential function solution $u(x,t)$ of the FODNLSequation by solving this matrix RH problem. In addition, we also obtained thatsome spectral functions admits a key global relationship.

Riemann-Hilbert problem associated with the fourth-order dispersive nonlinear Schr\"{o}dinger equation in optics and magnetic mechanics