A Numerical Approximation of Conformable Maxwell-Schrodinger Equations

A fractional Finite-Difference Time-Domain (FDTD) method for solving conformable Maxwell–Schrodinger equations is adapted from the classical FDTD method and fractional discretization. MaxwellSchrodinger equations model the interaction between external electromagnetic fields and quantum particles in inhomogeneous materials and the population inversion can be computed from their numerical solution. Here, parameter adjustments are shown via numerical experiments which are divided into two cases. In the first case, the fractional order parameter is set to one. Adjusting the time-step parameter to less than one increases the frequency of the population inversion, whereas adjusting the step-size parameter to less than one decreases the frequency of the population inversion. In the second case, the fractional order parameter is set to less than one. Increasing the frequency of the population inversion significantly, alongside a loss of smoothness and amplitude.