A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships
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 affair...
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| Format: | Article |
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MDPI AG
2017-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/19/7/375 |
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| author | Jagdev Singh Devendra Kumar Maysaa Al Qurashi Dumitru Baleanu |
| author_facet | Jagdev Singh Devendra Kumar Maysaa Al Qurashi Dumitru Baleanu |
| author_sort | Jagdev Singh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T00:26:19Z |
| format | Article |
| id | doaj.art-054e8cc972a1471caf868193b73df218 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T00:26:19Z |
| publishDate | 2017-07-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj.art-054e8cc972a1471caf868193b73df2182022-12-22T03:10:35ZengMDPI AGEntropy1099-43002017-07-0119737510.3390/e19070375e19070375A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic RelationshipsJagdev Singh0Devendra Kumar1Maysaa Al Qurashi2Dumitru Baleanu3Department of Mathematics, JECRC University, Jaipur, Rajasthan 303905, IndiaDepartment of Mathematics, JECRC University, Jaipur, Rajasthan 303905, IndiaDepartment of Mathematics, College of Science, King Saud University, Riyadh 11495, Saudi ArabiaDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4, Etimesgut 06790, TurkeyIn 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.https://www.mdpi.com/1099-4300/19/7/375Nonlinear fractional dynamical model of interpersonal and romantic relationshipCaputo fractional derivativeq-homotopy analysis methodSumudu transformAdomian’s decomposition method |
| spellingShingle | Jagdev Singh Devendra Kumar Maysaa Al Qurashi Dumitru Baleanu A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships Entropy Nonlinear fractional dynamical model of interpersonal and romantic relationship Caputo fractional derivative q-homotopy analysis method Sumudu transform Adomian’s decomposition method |
| title | A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships |
| title_full | A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships |
| title_fullStr | A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships |
| title_full_unstemmed | A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships |
| title_short | A Novel Numerical Approach for a Nonlinear Fractional Dynamical Model of Interpersonal and Romantic Relationships |
| title_sort | novel numerical approach for a nonlinear fractional dynamical model of interpersonal and romantic relationships |
| topic | Nonlinear fractional dynamical model of interpersonal and romantic relationship Caputo fractional derivative q-homotopy analysis method Sumudu transform Adomian’s decomposition method |
| url | https://www.mdpi.com/1099-4300/19/7/375 |
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