TY - JOUR

T1 - A Technique for Studying a Class of Fractional-Order Nonlinear Dynamical Systems

AU - Шерих, Ахмед Абделхамид Мохамед Ахмед

AU - Mahmoud, Gamal M.

AU - Farghaly, Ahmed A. M.

PY - 2017

Y1 - 2017

N2 - In this work, we propose a technique to study nonlinear dynamical systems with fractionalorder.The main idea of this technique is to transform the fractional-order dynamical systemto the integer one based on Jumarie’s modified Riemann–Liouville sense. Many systems in theinterdisciplinary fields could be described by fractional-order nonlinear dynamical systems, suchas viscoelastic systems, dielectric polarization, electrode-electrolyte polarization, heat conduction,resistance-capacitance-inductance (RLC) interconnect and electromagnetic waves. To dealwith integer order dynamical system it would be much easier in contrast with fractional-ordersystem. Two systems are considered as examples to illustrate the validity and advantages of thistechnique. We have calculated the Lyapunov exponents of these examples before and after thetransformation and obtained the same conclusions. We used the integer version of our exampleto compute numerically the values of the fractional-order and the system parameters at whichchaotic and hyperchaotic behaviors exist.

AB - In this work, we propose a technique to study nonlinear dynamical systems with fractionalorder.The main idea of this technique is to transform the fractional-order dynamical systemto the integer one based on Jumarie’s modified Riemann–Liouville sense. Many systems in theinterdisciplinary fields could be described by fractional-order nonlinear dynamical systems, suchas viscoelastic systems, dielectric polarization, electrode-electrolyte polarization, heat conduction,resistance-capacitance-inductance (RLC) interconnect and electromagnetic waves. To dealwith integer order dynamical system it would be much easier in contrast with fractional-ordersystem. Two systems are considered as examples to illustrate the validity and advantages of thistechnique. We have calculated the Lyapunov exponents of these examples before and after thetransformation and obtained the same conclusions. We used the integer version of our exampleto compute numerically the values of the fractional-order and the system parameters at whichchaotic and hyperchaotic behaviors exist.

KW - Fractional calculus

KW - chaotic; hyperchaotic

KW - Lyapunov exponents

U2 - 10.1142/S0218127417501449

DO - 10.1142/S0218127417501449

M3 - Article

VL - 27

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 09

M1 - 09

ER -