Exact Traveling Wave Solutions for the Space-Time Fractional Modified Third-Order KdV Equation Via an Improved Analytical Technique

This paper presents a novel application of the improved modified extended tanh-function method to derive exact traveling wave solutions for the space-time fractional modified third- order Korteweg-de Vries (KdV) equation. The fractional derivatives are considered in the con- formable fractional derivative form. The proposed method systematically reduces the nonlinear fractional partial differential equation to an ordinary differential equation, which is then solved using a generalized ansatz. A specific kink-type solitary wave solution is obtained in closed form. The results demonstrate the robustness and efficiency of the method for handling com- plex nonlinear fractional differential equations, providing valuable new solutions that enhance our understanding of wave propagation in fractional media.