Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method

The Ginzburg–Landau (GL) equation and the Ginzburg–Landau couple system are important models in the study of superconductivity and superfluidity. This study describes the q-homotopy analysis transform method (q-HATM) as a powerful technique for solving nonlinear problems, which has been successfully used with a set of mathematical models in physics, engineering, and biology. We apply the q-HATM to solve the Ginzburg–Landau equation and the Ginzburg–Landau coupled system and derive analytical solutions in terms of the q-series. Also, we investigate the convergence and accuracy of the obtained solutions. Our results show that q-HATM is a reliable and promising approach for solving nonlinear differential equations and provides a valuable tool for researchers in the field of superconductivity. Several graphs have been presented for the solutions obtained utilizing different levels of the fractional-order derivative and at various points in time.