On the numerical simulation and convergence study for system of non-linear fractional dynamical model of marriage

Shloof, A. M.; Ali, Halima; Khader, M. M.

doi:10.20852/ntmsci.2017.223

Cited by 4 publications

(4 citation statements)

References 18 publications

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“…They defined the fractional derivative in the Riemann-Liouville sense, and via the utilization of Bernstein polynomials, they converted the FDMM to a system of nonlinear algebraic equations, which were solved using Newton's iterative method. Khader et al [15] also solved the same model by implementing the Legendre spectral collocation method and affirmed the natural behavior of the present system. Singh et al [16] implemented a q-homotopy analysis method coupled with Sumudu transform and Adomian decomposition method to solve FDMM and comparison results with the existing literature are also included.…”

Section: Introductionsupporting

confidence: 61%

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

2019

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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.

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Section: Introductionsupporting

confidence: 61%

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

2019

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“…Studies in this regard may be challenging to achieve and may be confined to individual interests so that the mathematical model can be beneficial. As such, researchers are recently studying various interpersonal relationship dynamic models 4–8 …”

Section: Motivation and Outlinementioning

confidence: 99%

“…As such, researchers are recently studying various interpersonal relationship dynamic models. [4][5][6][7][8] The most recent love model is the Romeo and Juliet model. 3 Assume that we need to calculate Romeo's love or hate for Juliet R(t) and Juliet's love or hate for Romeo J(t) at any instance of time t. Positive values indicate love, and negative values signify hatred.…”

mentioning

confidence: 99%

Analysis of time‐fractional dynamical model of romantic and interpersonal relationships with non‐singular kernels: A comparative study

Jena

Chakraverty

Băleanu

et al. 2020

Math Methods in App Sciences

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The analysis of interpersonal relationships has started to become popular in the last few decades. Interpersonal relationships exist in many ways, including family, friendship, job, and clubs. In this manuscript, we have implemented the homotopy perturbation Elzaki transform method to obtain the solutions of romantic and interpersonal relationships model involving timefractional-order derivatives with non-singular kernels. The present method is the combination of the classical homotopy perturbation method and the Elzaki transform. This method offers a rapidly convergent series of solutions. The present approach explores the dynamics of love between couples. Validation and usefulness of the method are incorporated with new fractional-order derivatives with exponential decay law and with general Mittag-Leffler law. Obtained results are compared with the established solution defined in the Caputo sense. Further, a comparative study among Caputo and newly defined fractional derivatives are discussed.

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“…Jhinga and Daftardar in [20] presented a new numerical method for solving fractional delay differential equations along with its error analysis. Khader et al in [21] introduced an implementation of an efficient numerical method for solving the system of coupled non-linear fractional dynamical model of marriage. Their method was based on the spectral collocation method using Legendre polynomials.…”

mentioning

confidence: 99%

A robust computational framework for analyzing fractional dynamical systems

Sayevand¹,

Moradi²

2021

DCDS-S

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This study outlines a modified implicit finite difference method for approximating the local stable manifold near a hyperbolic equilibrium point for a nonlinear systems of fractional differential equations. The fractional derivative is described in the Caputo sense of order α (0 < α ≤ 1) which is approximated based on the modified trapezoidal quadrature rule of order O(△t 2−α). The solution existence, uniqueness and stability of the proposed method is discussed. Three numerical examples are presented and comparisons are made to confirm the reliability and effectiveness of the proposed method.

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On the numerical simulation and convergence study for system of non-linear fractional dynamical model of marriage

Cited by 4 publications

References 18 publications

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

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

Analysis of time‐fractional dynamical model of romantic and interpersonal relationships with non‐singular kernels: A comparative study

A robust computational framework for analyzing fractional dynamical systems

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