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A complex fractional mathematical modeling for the love story of Layla and Majnun

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  • Kumar, Pushpendra
  • Erturk, Vedat Suat
  • Murillo-Arcila, Marina

Abstract

In this article, we provide numerical simulations to show the importance and the effects of fractional order derivatives in psychological studies. As it is well-known, complex variables are more realistic for defining structures in different cases. In this paper, we evidence that such dynamics become more realistic when we use fractional derivatives. We study a non-integer order, non-linear mathematical model for defining a love story of Layla and Majnun (a couple in a romantic relationship). We exemplify all necessary practical calculations to study this serious psychological phenomena. The existence of the unique solution for the given model is exhibited. We use a very recent and strong modified Predictor-Corrector algorithm to evaluate the model structure. Stability of the proposed method is also given. We exemplify that the given complex fractional model is more realistic and represents reality more closely. The proposed model is very basic, significant, and efficient at introducing distinct natures by only replacing one control parameter. In this study, we found that in some of the cases there are stable limit cycles, in some cases periodic behaviours and sometimes transiently chaotic solutions exist which cannot be observed for integer order models at same parameter values. The principal contribution of this article is to exhibit the importance of non-integer order derivatives for analysing complex dynamics. The use of complex variables makes this study more effective because they have both magnitude and phase to better explore the love and can describe different emotions such as coexisting love and hate.

Suggested Citation

  • Kumar, Pushpendra & Erturk, Vedat Suat & Murillo-Arcila, Marina, 2021. "A complex fractional mathematical modeling for the love story of Layla and Majnun," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004458
    DOI: 10.1016/j.chaos.2021.111091
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    References listed on IDEAS

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    1. S. Sepehr Tabatabaei & Mohammad Javad Yazdanpanah & Sajad Jafari & Julien Clinton Sprott, 2014. "Extensions in dynamic models of happiness: effect of memory," International Journal of Happiness and Development, Inderscience Enterprises Ltd, vol. 1(4), pages 344-356.
    2. Nabi, Khondoker Nazmoon & Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Projections and fractional dynamics of COVID-19 with optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Erturk, Vedat Suat & Kumar, Pushpendra, 2020. "Solution of a COVID-19 model via new generalized Caputo-type fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Gao, Wei & Veeresha, P. & Baskonus, Haci Mehmet & Prakasha, D. G. & Kumar, Pushpendra, 2020. "A new study of unreported cases of 2019-nCOV epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
    6. Acay, Bahar & Inc, Mustafa, 2021. "Fractional modeling of temperature dynamics of a building with singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Kumar, Pushpendra & Erturk, Vedat Suat, 2021. "Environmental persistence influences infection dynamics for a butterfly pathogen via new generalised Caputo type fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Nabi, Khondoker Nazmoon & Abboubakar, Hamadjam & Kumar, Pushpendra, 2020. "Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Rubayyi T. Alqahtani & Shabir Ahmad & Ali Akgül, 2021. "Dynamical Analysis of Bio-Ethanol Production Model under Generalized Nonlocal Operator in Caputo Sense," Mathematics, MDPI, vol. 9(19), pages 1-21, September.
    2. Kumar, Pushpendra & Govindaraj, V. & Erturk, Vedat Suat, 2022. "A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Zulqurnain Sabir & Juan L. G. Guirao, 2023. "A Soft Computing Scaled Conjugate Gradient Procedure for the Fractional Order Majnun and Layla Romantic Story," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    4. Zulqurnain Sabir & Atef F. Hashem & Adnène Arbi & Mohamed A. Abdelkawy, 2023. "Designing a Bayesian Regularization Approach to Solve the Fractional Layla and Majnun System," Mathematics, MDPI, vol. 11(17), pages 1-13, September.
    5. Kumar, Pushpendra & Erturk, Vedat Suat & Vellappandi, M. & Trinh, Hieu & Govindaraj, V., 2022. "A study on the maize streak virus epidemic model by using optimized linearization-based predictor-corrector method in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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