A Novel Mathematical Model on Human Feelings via Fractional Operator with Non-singular Kernel

Abstract

Mathematics is a set of tools that try to describe human life and the universe which include symmetrical and asymmetrical structures by using various methods, provide analyzes and make predictions for the solution of problems by reaching syntheses. Considering the chaotic nature of life and human feelings, mathematical models that offer descriptions within a certain symmetrical order gain importance. Fractional derivative and integral operators introduced in fractional analysis are very effective and useful concepts that serve these purposes. In this study, based on the analysis of a literary work, an equation system that models human feelings is discussed with the help of the Caputo-Fabrizio fractional operator, which has a non-singular kernel. The existence and uniqueness of the solution of the system of equations included in this model and the compatibility of the numerical solutions with the analysis of the literary work according to different parameter values with the help of simulations are discussed.