Love Dynamical Model with persepectives of Piecewise Differential Operators

TL;DR

This paper introduces a novel love dynamical model using piecewise derivatives, including fractional and stochastic types, to better capture complex emotional behaviors and chaos in romantic relationships.

Contribution

It presents a new approach combining piecewise derivatives with love models, demonstrating existence, uniqueness, and numerical analysis of disordered emotional patterns.

Findings

Piecewise derivatives effectively model chaotic emotional dynamics.

Numerical simulations show diverse emotional scenarios.

Fractional derivatives influence the complexity of love dynamics.

Abstract

For love dynamical models, a new idea combining piecewise concept for integer-order, stochastic, and fractional derivatives is presented in order to capture the chaos and several crossover emotional scenerios. Under the assumptions of linear growth and Lipschitz condition, the fixed-point theorem explain the uniqueness and existence to the models under the investigation. The piecewise derivatives were approximated utilising the Lagrange interpolation method, and the computer results were demonstrated numerically for several values of order $\alpha$. It was observed that the recently presented new idea in love dynamical models can represent disordered emotional patterns in passionate loving partnerships.