Extensions in dynamic models of happiness: effect of memory

Abstract

Due to its more dynamical richness, fractional calculus is used to derive a dynamic model of happiness in response to real life events and under different mental conditions. Previous models are extended by using fractional derivatives whose order may vary in time. This extension helps to describe memory-dependent behaviors. Since the proposed model is an extension of the former models, it includes all of their merits. As simulations show, the new model can be utilized to describe the effect of short term memory on happiness when memory decays or is lost suddenly, similar to what happens in electroconvulsive therapy.

RETRACTED ARTICLE: A fractional order nonlinear model of the love story of Layla and Majnun

“…Psychology is one of the scientific learning processes of the mind, which is reported in the psychological associations of America 1 – 4 . Few psychologists and the mathematicians have introduced the system models to present the romantic relationships 5 – 7 .…”

Consensus of Multiagent Systems Described by Various Noninteger Derivatives

“…The broad variety of applications that the aforementioned fractional derivatives have had is remarkable: from quantum mechanics, Laskin [13], to control theory, Baleanu, Machado, and Luo [14], and study of human memory and emotions, Tabatabaei, Yazdanpanah, Jafari, and Sprott [15]. In general, these and other problems involving differential equations of fractional order are complicated to approach and in many cases there are no analytical or numerical schemes to solve them.…”

Layla and Majnun: a complex love story

“…There is a growing interest in using mathematics and computational methods in psychology [1][2][3][4][5][6][7][8][9][10]. Some mathematicians and psychologists have introduced mathematical models for romantic relationships [3,7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

“…Some mathematicians and psychologists have introduced mathematical models for romantic relationships [3,7,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. A difficulty in love modeling is quantifying love in some meaningful way [27].…”

“…In [26], a series of love models was provided describing different kinds of romantic relationships. Fractional-order models [7,29] and time-delay models [14] have been considered as a way to include memory. The goal of most of these works is to illustrate the complexity that can arise in even minimal dynamical models when the equations are nonlinear.…”