Numerical and mathematical analysis of induction motor by means of AB-fractal-fractional differentiation actuated by drilling system

The quality of electric induction motors for its high number of applications can be compared with traditional motor for the check of accuracy of physical and psychological discomforts. A mathematical analysis is performed to study the chaotic phenomena of drilling system actuated by induction motor by means of newly defined fractal-fractional differentiations. The mathematical modeling is described by focusing the drilling system consisting of two disks connected to each other by a steel string in which upper disk is actuated by DC-motor and lower disk with friction force. The derived dynamical mathematical model of drilling system actuated by induction motor based on ordinary differential equations is fractionalized with fractal differential operator of Atangana-Baleanu. For the sake of confirmation of drill string failures and breakdowns, the numerical simulations are performed via novel effective technique of linear multi-step integration method (Adams-Bashforth-Moulton method). At the end, the fractional, fractal, and fractal-fractional chaotic behaviors and phase portraits have disclosed various resemblances and metamorphoses.