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

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 fraction...

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Main Authors: Muhammad Marwan, Gauhar Ali, Ramla Khan
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2022/3505634
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author Muhammad Marwan
Gauhar Ali
Ramla Khan
author_facet Muhammad Marwan
Gauhar Ali
Ramla Khan
author_sort Muhammad Marwan
collection DOAJ
description 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.
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spelling doaj-art-f25cad6045784d29bf92d93791331f0c2025-02-03T01:20:19ZengWileyComplexity1099-05262022-01-01202210.1155/2022/3505634Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical SystemMuhammad Marwan0Gauhar Ali1Ramla Khan2College of Mathematics and Computer ScienceDepartment of MathematicsSchool of Environment Earth and Ecosystem Sciences (EEES) SchoolThis 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.http://dx.doi.org/10.1155/2022/3505634
spellingShingle Muhammad Marwan
Gauhar Ali
Ramla Khan
Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
Complexity
title Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
title_full Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
title_fullStr Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
title_full_unstemmed Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
title_short Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System
title_sort existence of solution and self exciting attractor in the fractional order gyrostat dynamical system
url http://dx.doi.org/10.1155/2022/3505634
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AT gauharali existenceofsolutionandselfexcitingattractorinthefractionalordergyrostatdynamicalsystem
AT ramlakhan existenceofsolutionandselfexcitingattractorinthefractionalordergyrostatdynamicalsystem