A Modified Fractional Differential Love Model

[1] F. A. Alawad, E. A. Yousif, and I. A. Arbab, A new technique of Laplace iteration method for solving space-time fractional telegraph equations, International Journal of Differential Equations, Article ID 256593, 10 pages, doi: 10.1155/2013/256593, (2013).10.1155/2013/256593Search in Google Scholar

[2] A. Cheriff, and K. Barley, Stochastic nonlinear dynamics of interpersonal and romantic relationships, Applied Mathematics and Computation, 217(13), 6273-6281, doi:10.1016/j.amc.2010.12.117, (2011).10.1016/j.amc.2010.12.117,(2011)Open DOISearch in Google Scholar

[3] J. M. Gottman, J. D. Murray, C. C. Swanson, R. Tyson,, and K. R. Swanson, The Mathematics of marriage, Cambridge, MA: MIT Press, (2005).Search in Google Scholar

[4] J. Gottman, S. Catherine, and S. Kristin, A general systems theory of marriage: Nonlinear difference equation modeling of marital interaction, Personality and Social Psychology Review 6(4), 326-340, (2002).Search in Google Scholar

[5] A. Gragnani, S. Rinaldi, and F. Gustav, Cyclic dynamics in romantic relationships, International Journal of Bifurcation and Chaos. 7(11), 2611-2619, (1997).10.1142/S0218127497001771Search in Google Scholar

[6] R. Gu, and Y. Xu, Chaos in a fractional-order dynamical model of love and its control In: Li S., Wang X., Okazaki Y., Kawabe J., Murofushi T., Guan L. (Eds) Nonlinear Mathematics for Uncertainty and its Applications, Advances in Intelligent and Soft Computing, vol. 100, pp. 349-356. Springer, Berlin, Heidelberg (2011, January).10.1007/978-3-642-22833-9_42Search in Google Scholar

[7] W. Liu, and K. Chen, Chaotic behavior in a new fractional-order love triangle system with competition, Journal of Applied Analysis and Computation, 5(1), 103-113.doi:10.11948/2015009, (2015).10.11948/2015009Search in Google Scholar

[8] F. Mohammadi, Numerical solution of Bagley-Tovik equation using Chebyshev operational matrix of fractional derivative, International Journal of Advances in Applied Mathematics and Mechanics, 2(1), 83-91, ISSN:2347-2529, (2014).Search in Google Scholar

[9] O.S Odetunde, and O.A Taiwo, An algorithm for the approximation of fractional differential-algebraic equations with Caputo-type derivatives, Journal of Applied & Computational Mathematics, 4(5),242, doi: 10.4172/2168-9679.1000242, (2015).10.4172/2168-9679.1000242,(2015)Open DOISearch in Google Scholar

[10] E. Okyere, F. T. Oduro, S. K. Amponsah, I. K. Dontwi, and N. K. Frempong, Fractional order SIR model with constant population, British Journal of Mathematics and Computer Science, 14(2) 1-12, doi: 10.9734/BJMCS/2016/23017, (2016).10.9734/BJMCS/2016/23017Search in Google Scholar

[11] N. Ozalp, and I. Koca, A fractional order nonlinear dynamical model of interpersonal relationships, Advances in Difference Equations, 2, 1-7, (2012).10.1186/1687-1847-2012-189Search in Google Scholar

[12] R. P. Paul, S. L. Larry, M. G. John, D. N. Michael, and S. Jessica, A mathematical model of psychotherapy: An investigation using dynamic non-linear equations to model the therapeutic relationship, Psychoterapy Research, doi:10.1080/10503307.2011.622314, (2011).10.1080/10503307.2011.622314,(2011)Open DOISearch in Google Scholar

[13] L. Song, and J. Yang, Chaos control and synchronization of dynamical model of happiness with fractional order, Conference proceeding of the 4th IEEE Conference on Industrial Electronics and Applications (ICIEA), Institute of Electrical and Electronics Engineers, Inc. 919 924 10.1109/ICIEA.2009.5138330. Retrieved from ieeexplore.ieee.org/document/5138330/,(2009, May 29).10.1109/ICIEA.2009.5138330Search in Google Scholar

[14] L. Von Bertalanffy, General system theory, New York: Family Psychology, (9), 110-130, (1968).Search in Google Scholar

[15] D. Weigel, and C. Murray, The paradox of stability and change in relationships: What does chaos theory offer for the study of romantic relationships?, 17(3), 425-449, (2000).Search in Google Scholar