Fractional Meissner-Ochsenfeld effect in superconductors

摘要

Fractional calculus (FC) is a valuable tool in the modeling of many phenomena, and it has become a topic of great interest in science and engineering. This mathematical tool has proved its efficiency in modeling the intermediate anomalous behaviors observed in different physical phenomena. The Meissner-Ochsenfeld effect describes the levitation of superconductors in a nonuniform magnetic field if they are cooled below critical temperature. This paper presents analytical solutions of the fractional London equation that describes the Meissner-Ochsenfeld effect considering the Liouville-Caputo, Caputo-Fabrizio-Caputo, Atangana-Baleanu-Caputo, fractional conformable derivative in Liouville-Caputo sense and Atangana-Koca-Caputo fractional-order derivatives. Numerical simulations were obtained for different values of the fractional-order.