Numerical simulation for time-fractional nonlinear coupled dynamical model of romantic and interpersonal relationships

[摘要] The objective of this paper is to study the nonlinear coupled dynamical fractional model of romantic and interpersonal relationships using fractional variation iteration method (FVIM) and fractional homotopy perturbation transform method (FHPTM). These procedures inspect the dynamics of love affairs among couples. Sufficient conditions for their convergence and error estimates are established. Obtained results are compared with the existing and recently developed methods. It is interesting to observe that these methods also work for those fractional models that do not have an exact solution. Results for different fractional values of time derivative are discussed with the help of figures and tables. Figures are drawn using Maple package. Test examples are provided to illustrate the accuracy and competency of the proposed schemes. Results divulge those schemes that are attractive, accurate, easy to use and highly effective.

[学科分类] 物理（综合）

[关键词] Fractional variation iteration method;fractional homotopy perturbation transform method;Caputo fractional derivative;He’s polynomials