On the Solution of an Imprecisely Defined Nonlinear Time-Fractional Dynamical Model of Marriage

The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normaliz...

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Bibliographic Details
Published in:Mathematics (Basel) 2019-08, Vol.7 (8), p.689
Main Authors: Jena, Rajarama, Chakraverty, Snehashish, Baleanu, Dumitru
Format: Article
Language:English
Subjects:
Couples
Divorce
double-parametric form
Dynamic models
Dynamical systems
Food science
fractional calculus
fractional dynamical model of marriage
FRDTM
Fuzzy sets
Hypotheses
Initial conditions
Investigations
Love
Marriage
Mathematical models
Numerical analysis
Personal relationships
triangular fuzzy number
Uncertainty
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Summary:The present paper investigates the numerical solution of an imprecisely defined nonlinear coupled time-fractional dynamical model of marriage (FDMM). Uncertainties are assumed to exist in the dynamical system parameters, as well as in the initial conditions that are formulated by triangular normalized fuzzy sets. The corresponding fractional dynamical system has first been converted to an interval-based fuzzy nonlinear coupled system with the help of a single-parametric gamma-cut form. Further, the double-parametric form (DPF) of fuzzy numbers has been used to handle the uncertainty. The fractional reduced differential transform method (FRDTM) has been applied to this transformed DPF system for obtaining the approximate solution of the FDMM. Validation of this method was ensured by comparing it with other methods taking the gamma-cut as being equal to one.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7080689