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

Author

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  • Khalid K. Ali
  • M. Maneea
  • Mohamed S. Mohamed
  • Yusuf Gurefe

Abstract

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.

Suggested Citation

  • Khalid K. Ali & M. Maneea & Mohamed S. Mohamed & Yusuf Gurefe, 2023. "Solving Nonlinear Fractional Models in Superconductivity Using the q-Homotopy Analysis Transform Method," Journal of Mathematics, Hindawi, vol. 2023, pages 1-23, August.
    • Handle: RePEc:hin:jjmath:6647375
    DOI: 10.1155/2023/6647375
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