The major purpose of this study is to seek diverse soliton solutions to the nonlinear discretized mKdv lattice system including fractional-order in the sense of conformable derivative. The rational forms of trigonometric, hyperbolic, and Jacobi elliptic functions are employed to generate these exact solutions. The auxiliary rational structure is used for obtaining exact solutions which provide solitary, periodic, and soliton varieties of traveling wave solutions. The solutions obtained will provide a comprehensive study of this model and any related events
