Dynamical Analysis of the Irving-Mullineux Oscillator Equation of Fractional Order

Abstract

Objective: Objective of this work is to study the fractional counterpart of the Irving-Mullineux nonlinear oscillator equation and compare the result with the integer order equation theoretically as well as numerically. Methods For analytical results we use contraction principle to show the existence of the solution and then eigenvalue analysis to check the stability of the equilibrium points. Adams-type predictor-corrector method has been used for the numerical simulation. Results Stability conditions are given in terms of the parameter α. Numerical simulations indicate that the fractional differential equation shows stable result compared to their integer counterpart. Conclusion The obtained results shown that the stability depends on the parameter α and numerical results indicate that the fractional system may stabilize the corresponding integer order system. The results obtained also show that when α→1, the solutions of fractional equation reduce to the solution of corresponding integer equation. Practice Fractional order system can be taken while analyzing the oscillatory behavior of certain system. It is more general and sometimes gives better approximate results. Implications The fractional order equation may give better results than integer order equation when applied to real life problems. © 2014 Elsevier B.V.