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Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators

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  • Yusuf, Abdullahi
  • Qureshi, Sania
  • Feroz Shah, Syed

Abstract

Economic agents remember the stories of changes of exogenous and endogenous variables leading researchers to employ fractional operators which inherently possess non-locality, Markovian and/or non-Markovian properties and short and long term memory effects. This research analysis revolves around the comparative study of an autonomous dynamical financial system using classical approach of differentiation and also contemporary tools from fractional calculus known as Caputo (α), Caputo–Fabrizio–Caputo (β) and the Atangana–Baleanu–Caputo (γ) operators. Firstly, the standard financial model is fractionalyzed taking different fractional-order parameter for each autonomous equation in all three models and obtained the new financial models with three operators under consideration. Fixed point theory shows that the fractional-order models have unique solution in the Banach space. Numerical simulations of the fractional order models apparently depict the varying interesting phenomena such as periodicity, fixed points and chaotic routes in two and three dimensional illustrations not obtainable via standard differentiation. In particular, the financial model with Atangana–Baleanu–Caputo operator represents comparatively fewer number of fluctuations over both small and large time scales and thus is said to possess better stability characteristics.

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  • Yusuf, Abdullahi & Qureshi, Sania & Feroz Shah, Syed, 2020. "Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    • Handle: RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305090
    DOI: 10.1016/j.chaos.2019.109552
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    References listed on IDEAS

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    1. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    2. Abro, Kashif Ali & Khan, Ilyas & Nisar, Kottakkaran Sooppy, 2019. "Novel technique of Atangana and Baleanu for heat dissipation in transmission line of electrical circuit," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 40-45.
    3. Abu Arqub, Omar & Al-Smadi, Mohammed, 2018. "Atangana–Baleanu fractional approach to the solutions of Bagley–Torvik and Painlevé equations in Hilbert space," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 161-167.
    4. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    5. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    6. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    7. Arqub, Omar Abu & Maayah, Banan, 2019. "Fitted fractional reproducing kernel algorithm for the numerical solutions of ABC – Fractional Volterra integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 394-402.
    8. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    9. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    10. Ullah, Saif & Altaf Khan, Muhammad & Farooq, Muhammad, 2018. "A fractional model for the dynamics of TB virus," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 63-71.
    11. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
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    Cited by:

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    3. Juan J. Gude & Pablo García Bringas, 2022. "A Novel Control Hardware Architecture for Implementation of Fractional-Order Identification and Control Algorithms Applied to a Temperature Prototype," Mathematics, MDPI, vol. 11(1), pages 1-40, December.
    4. Zhenduo Sun & Nengneng Qing & Xiangzhi Kong, 2023. "Asymptotic Hybrid Projection Lag Synchronization of Nonidentical Variable-Order Fractional Complex Dynamic Networks," Mathematics, MDPI, vol. 11(13), pages 1-17, June.

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