<p>This study investigates the fractional-order Benjamin–Ono equation by constructing a comprehensive set of analytical solutions based on Jacobi elliptic functions. Utilizing a wave transformation approach, eleven distinct exact solutions are derived, each corresponding to a different Jacobi elliptic function, including ‘sn’, ‘cn’, ‘dn’, ‘sc’, ‘sd’, and others. The resulting solutions are not only presented analytically but also examined through detailed graphical representations and physical interpretations. These analyses reveal the underlying dynamics of periodic, solitary, and blow-up type wave structures governed by fractional nonlocality. The diversity of wave profiles obtained highlights the flexibility and strength of the Jacobi elliptic framework in modeling complex, memory-driven behaviors in nonlinear fractional systems. This work provides a systematic and physically meaningful classification of solution types, contributing to the theoretical understanding of fractional wave phenomena and offering potential for future applications in dispersive and nonlocal media.</p>