Mathematical modelling and analysis of love dynamics: A fractional approach

Kolade M. Owolabi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 525, issue C, 849-865

Abstract: A range of new fractional-order love dynamics is modelled in this paper using the Caputo (power-law), Caputo–Fabrizio (exponential decay-law) and Atangana–Baleanu (Mittag-Leffler-law) fractional operators. We utilize the new fractional Adams–Bashforth schemes for the approximation of these derivatives. This method was developed with the standard differentiation technique by applying the fundamental theorem of calculus and taking the difference of two times levels at t=(tn,tn+1). The stability analysis applies the theory of classical order differential equations and dynamical system. The Existence and uniqueness of solution of fractional dynamics is proved by adopting the fixed-point theorem. Numerical results presented for various α− values justify the theoretical findings. It was observed that modelling of interpersonal and romantic love affairs with fractional derivative could exhibit some strange emotional attractors.

Keywords: Atangana–Baleanu derivative; Caputo derivative; Caputo–Fabrizio derivative; Fractional love dynamics; Existence and uniqueness; Numerical simulation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:525:y:2019:i:c:p:849-865

DOI: 10.1016/j.physa.2019.04.024

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