New Local Fractional Mohand–Adomian Decomposition Method for Solving Nonlinear Fractional Burger’s Type Equation

In this article, we address the challenge of solving the nonlinear fractional Burger’s KdV equation, time-fractional Burger’s equation, and the fractional modified Burger’s equation. This is achieved by employing the Caputo and conformable derivatives. To tackle these equations, we introduce a new numerical method which is the combination of the local fractional Mohand transform and the Adomian decomposition method. This choice is driven by its straightforward methodology and reduced computational complexity. Moreover, to demonstrate the versatility of this technique, we provide several illustrative examples along with their corresponding exact or approximate solutions. These solutions are accompanied by graphical representations, further enhancing the clarity of the presented approach.