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Complex dynamics and control of a novel physical model using nonlocal fractional differential operator with singular
A E Matouk1,2, I Khan1
1Department of Mathematics, College of Science, Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia.
Abstract:
Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed. A sufficient condition is used to prove that the solution of the proposed system exists and is unique in a specific region. Conditions for the approximating periodic solution in this model via Hopf bifurcation theory are discussed. Chaotic dynamics are found in the commensurate system for a wide range of fractional orders. The Lyapunov exponents and Lyapunov spectrum of the model are provided. Suppressing chaos in this system is also achieved via two different methods.
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