Approximate Analytical Methods for a Fractional-Order Nonlinear System of Jaulent–Miodek Equation with Energy-Dependent Schrödinger Potential

In this paper, we study the numerical solution of fractional Jaulent–Miodek equations with help two modified methods: coupled variational iteration transformation technique and Adomian decomposition technique. The equation has applications in several related fields physics, including control theory dynamical systems, anomalous transport, image signal processing, financial modelings, nanotechnology, viscoelasticity, nanoprecipitate growth solid solutions, random walk, modeling for shape memory polymers, condensed matter fluid mechanics, optics plasma physics. results are presented as a series quickly converging solutions. Analytical solutions have been performed absolute error to confirm proposed methodologies trustworthy accurate. generated visually illustrated guarantee validity applicability taken into consideration algorithm. study’s findings show that, compared alternative analytical approaches analyzing non-linear equations, transform method computationally very efficient