Conformable operator approach to solving time-fractional Jaulent-Miodek system within analytical methods

This paper examines the time-fractional Jaulent-Miodek coupled system which is a vital model in plasma physics and nonlinear wave equations. In solving this system, we use some advanced analytical tools such as Elzaki Adomian decomposition method (EADM), and reduced differential transform method (RDTM) to solve it in the domain of fractional orders. This is coupled with the addition of a conformable operator which means that the accuracy and flexibility of the solution method is increased and the fractional derivatives involved are more thoroughly treated. Our techniques provide approximate analytical solutions to the time-fractional coupled Jaulent-Miodek system and we illustrate the use of our methods by small numerical experiments. In the findings, it is observed that EADM and RDTM have substantial benefits of convergence and computational efficiency. The piece of work also helps to develop numerical methods of applying and solving fractional differential equations especially in the mode of plasma dynamics, and, also, it further gives insight about the behavior of nonlinear systems together with fractional-order derivatives.