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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.

Original publication

DOI

10.1155/2022/3505634

Type

Journal article

Journal

Complexity

Publisher

Wiley

Publication Date

01/2022

Volume

2022