Mathematical modelling of fiber optic cable with an electro-optical cladding by incommensurate fractional-order differential equations

In this study, the mathematical model through incommensurate fractional-order differential equations in Caputo meaning are presented for time-dependent variables given as the numerical aperture, critical angle, and acceptance angle characteristics of a fiber optic cable with electro-optical cladding. The qualitative analysis including the existence and stability of the equilibrium points of the proposed model has been made according to the used parameters, and then, the results obtained from this analysis are supported through numerical simulations by giving the possible values that can be obtained from experimental studies to these parameters in the model. In this way, a stable equilibrium point of the system for the core refractive index, cladding refractive index and electrical voltage is obtained according to the threshold parameter. Thus, the general formulas for the critical angle, acceptance angle and numerical aperture have been obtained when this fixed point is stable.