A novel study of analytical solutions of some important nonlinear fractional differential equations in fluid dynamics

The space-time fractional Burger-like equation and the space-time coupled Boussinesq equation with conformable derivative, both of which are significant in fluid dynamics, are investigated in this work using the improved [Formula: see text] method. The process works effectively and produces soliton solutions. The method was successfully and consistently implemented with Maple, a symbolic computing tool. The solutions also contain a few of graphics. Numerous novel exact solutions to these equations, distinct from those found earlier with the proposed approach, have been provided. The study’s findings add to the body of knowledge by offering insightful justifications for various types of nonlinear systems. The results demonstrated the value of the proposed method as a mathematical tool and the ease, dependability, and speed increases that result from carrying out these tasks using a symbolic computing program. Notably, it applies to many nonlinear evolution problems in mathematical physics.