The space-time fractional modified Benjamin-Bona-Mahony problem is reduced and analytically solved using the fractional sub-equation approach. The RiemannLiouville derivative as modified by Jumarie is examined. Graphical representations of periodic, kink, and multi-soliton solutions are shown as examples of the obtained solutions. Using this method, researchers may create new, one-of-a-kind solutions to a wide variety of nonlinear fractional partial differential equations.