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

Abdullahi Yusuf, Sania Qureshi and Syed Feroz Shah

Chaos, Solitons & Fractals, 2020, vol. 132, issue C

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.

Keywords: Non-Markovian; Fixed point theory; Deterministic models; Time invariant; Non-locality (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:132:y:2020:i:c:s0960077919305090

DOI: 10.1016/j.chaos.2019.109552

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