Analytical Multiple Soliton Solutions for a Class of Coupled Fractional Order Under Time‐Dependent Variable Coefficient Korteweg–de Vries

ABSTRACT For linked fractional modified Korteweg–de Vries (mKdV) systems, in which the coefficient is a time‐dependent variable, we investigate exact multiple soliton solutions. Based on the similarity transformation and the Hirota bilinear technique, we report both multiple wave kink and single wave kink solutions for two different models of fractional mKdV with time‐dependent variable coefficients. We use the fractional Hirota bilinear technique to compute analytical solutions for modified coupled space–time–fractional KdV systems. We construct many kink waves for the proposed fractional differential models under study. For the treatment of nonlinear differential models of integer and fractional orders, the Hirota bilinear technique provides a straightforward and promising method. Recently, researchers have been using symbolic computation—like Maple—to perform these calculations. We investigated whether the results demonstrate the simplicity, effectiveness, and ease of computation of the approach for a range of engineering and physics models. The flexible and random selection of the fractional orders allows us to build deeper structures. Soliton modifications based on fractional order changes enable further applications in applied science.