Premium
Stability and chaos control of regularized Prabhakar fractional dynamical systems without and with delay
Author(s) -
Eshaghi Shiva,
Khoshsiar Ghaziani Reza,
Ansari Alireza
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5509
Subject(s) - mathematics , control theory (sociology) , attractor , nonlinear system , stability (learning theory) , chaotic , exponential stability , function (biology) , controller (irrigation) , lyapunov function , control (management) , mathematical analysis , computer science , artificial intelligence , machine learning , physics , quantum mechanics , evolutionary biology , agronomy , biology
In this paper, we studied the stabilization of nonlinear regularized Prabhakar fractional dynamical systems without and with time delay. We establish a Lyapunov stabiliy theorem for these systems and study the asymptotic stability of these systems without design a positive definite function V (without considering the fractional derivative of function V is negative). We design a linear feedback controller to control and stabilize the nonautonomous and autonomous chaotic regularized Prabhakar fractional dynamical systems without and with time delay. By means of the Lyapunov stability, we obtain the control parameters for these type of systems. We further present a numerical method to solve and analyze regularized Prabhakar fractional systems. Furthermore, by employing numerical simulation, we reveal chaotic attractors and asymptotic stability behaviors for four systems to illustrate the presented theorem.