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 behaviours. 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 utilised to describe the effect of short-term memory on happiness when memory decays or is lost suddenly, similar to what happens in electroconvulsive therapy.