A Fractional-Differential Approach to Numerical Simulation of Electron-Induced Charging of Ferroelectrics

The paper proposes a fractional-differential modification of the mathematical model of theprocess of nonstationary charging of polar dielectric materials under conditions of irradiation withmedium-energy electron beams. The mathematical formalization is based on a sphericallysymmetric diffusion–drift equation with a fractional time derivative. An implicit finite-differencescheme is constructed using the Caputo derivative approximation. An application program hasbeen developed in Matlab softwarethat implements the designed computational algorithm. Verification of an approximate solution ofthe problem is demonstrated using a test example. The results of computational experiments toevaluate the characteristics of field effects of injected charges in ferroelectrics when varying theorder of fractional differentiation in subdiffusion regimes are presented.