Abstract
This study uses efficient techniques to evaluate a non-linear system of Korteweg-de Vries (KdV) equations with fractional Caputo Fabrizio derivative, including the modified decomposition approach and the novel iterative transform method. The system of KdV equations and the modify scheme of KdV equations used as a model in non-linear physical processes emerging in biology, chemistry, physics and sciences are the non-linear fractional coupled systems explored in this present analysis. Approximate analytical outcomes are represented as a series with simple components, and some features revealed a proper dependency on the fractional-order derivatives' values. An examination of convergence and uniqueness is performed. Three test cases for the analytic findings of the fractional-order KdV equations are supplied to help understand the analytical technique of both methods. Furthermore, the efficiency of the aforementioned operations, as well as the decrease in computations, allow for a larger application. It is also demonstrated that the present methodology's conclusions are in close agreement with the precise answers. With few computations, the series result obtained using this approach has been proven to be accurate and dependable. For various fractional-order values, numerical simulations for derived solutions are described.