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


Ersoy B., Daşbaşı B., Aslan E.

An International Journal of Optimization and Control: Theories & Applications, vol.0, no.0, pp.1-11, 2024 (Scopus)

Abstract

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 accep-tance 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.