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This article presents the phase dynamics of an inline long Josephson junctionin voltage state under the influence of constant external magnetic field.Fractional calculus approach is used to model the evolution of the phasedifference between the macroscopic wave functions of the two superconductorsacross the junction. The governing non-linear partial differential equation isthen solved using finite difference-finite element schemes. Other quantities ofinterest like Josephson current density and voltage across the junction arealso computed. The effects of various parameters in the model on phasedifference, Josephson current density and voltage are analyzed graphically withthe help of numerical simulations.

Fractional calculus approach for the phase dynamics of Josephson junction under the influence of magnetic field