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

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

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Department of Mathematics, JECRC University, Jaipur, Rajasthan 303905, India
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Department of Mathematics, College of Science, King Saud University, Riyadh 11495, Saudi Arabia
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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)
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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
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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).

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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.

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