Fractional calculus approach for the phase dynamics of Josephson junction.

• Phase dynamics of inline Josephson junction in voltage state is discussed. • Phase difference between the wave functions is analyzed via fractional calculus. • Hereditary effects for phase dynamics of Josephson junction are explored. • Finite element scheme is used for the simulations of governing equations. This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations. [ABSTRACT FROM AUTHOR]