Next Article in Journal
Comparative Analysis of Jüttner’s Calculation of the Energy of a Relativistic Ideal Gas and Implications for Accelerator Physics and Cosmology
Next Article in Special Issue
Toward a Theory of Industrial Supply Networks: A Multi-Level Perspective via Network Analysis
Previous Article in Journal
Transfer Entropy for Nonparametric Granger Causality Detection: An Evaluation of Different Resampling Methods
Previous Article in Special Issue
Two Approaches to Obtaining the Space-Time Fractional Advection-Diffusion Equation
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(7), 375; doi:10.3390/e19070375

A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships

1
Department of Mathematics, JECRC University, Jaipur, Rajasthan 303905, India
2
Department of Mathematics, College of Science, King Saud University, Riyadh 11495, Saudi Arabia
3
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4, Etimesgut 06790, Turkey
4
Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest 76911, Romania
*
Author to whom correspondence should be addressed.
Received: 28 May 2017 / Revised: 4 July 2017 / Accepted: 19 July 2017 / Published: 22 July 2017
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
View Full-Text   |   Download PDF [1978 KB, uploaded 24 July 2017]   |  

Abstract

In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian’s decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice. View Full-Text
Keywords: Nonlinear fractional dynamical model of interpersonal and romantic relationship; Caputo fractional derivative; q-homotopy analysis method; Sumudu transform; Adomian’s decomposition method Nonlinear fractional dynamical model of interpersonal and romantic relationship; Caputo fractional derivative; q-homotopy analysis method; Sumudu transform; Adomian’s decomposition method
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Singh, J.; Kumar, D.; Qurashi, M.A.; Baleanu, D. A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships. Entropy 2017, 19, 375.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top