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Existence of Solution and Self‐Exciting Attractor in the Fractional‐Order Gyrostat Dynamical System

Author

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  • Muhammad Marwan
  • Gauhar Ali
  • Ramla Khan

Abstract

This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional‐order gyrostat model with the help of a fixed‐point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel‐filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. Moreover, this iterative scheme is injected into algorithms for a system of integer order dynamical systems to observe Lyapunov exponents and a bifurcation diagram for our proposed fractional‐order dynamical model. Furthermore, we obtained five equilibrium points, including four unstable spirals and one saddle node, using local dynamical analysis which acted as self‐exciting attractors and a separatrix in a global domain.

Suggested Citation

  • Muhammad Marwan & Gauhar Ali & Ramla Khan, 2022. "Existence of Solution and Self‐Exciting Attractor in the Fractional‐Order Gyrostat Dynamical System," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3505634
    DOI: 10.1155/2022/3505634
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