Abstract This work studies the tempered fractional (2+1)-dimensional Konopelchenko-Dubrovsky system. The tempered fractional derivative considered in the context of Caputo tempered derivative. We develop a new method based on the Laplace transform, with an improvement on the residual power series method, to handle the governing system and reveal its dynamics. We present a theoretical and experimental analysis to investigate the convergence of the developed method. Different initial conditions and values for the system parameters were used, and the resulting solutions were presented in 3D and 2D panels. A comparison of the discovered approximate solutions with the exact solutions is presented to investigate the efficiency and accuracy of the proposed approach. In addition, the effect of the tempered coefficient and fractional derivative on the behavior of the derived solutions is investigated. To connect the mathematical results with physical insights, a physical example is presented for modeling intrinsic perturbations in a highly coupled magneto plasma (tokamak plasma) to describe the propagation of nonlinear waves in this plasma. Using the discovered solutions for the governing system, the control of perturbations within the plasma and external factors is investigated using the tempered coefficient and fractional derivative. Our results demonstrate the efficiency and reliability of the proposed method for handling the governing system and confirm the possibility of describing complex physical phenomena in several domains using the tempered fractional (2+1)-dimensional Konoplychenko-Dubrovsky system.
Alshammari et al. (Fri,) studied this question.