A nonlinear system related to investment under uncertainty solved using the fractional pseudo-Newton method

TL;DR

This paper introduces a fractional pseudo-Newton method to numerically solve a nonlinear algebraic system derived from an investment under uncertainty model, enhancing solution techniques for complex economic systems.

Contribution

The paper presents a novel fractional iterative method leveraging fractional calculus properties to solve nonlinear systems related to investment decision models.

Findings

Successfully solved a nonlinear algebraic system from an investment model.

Demonstrated the effectiveness of the fractional pseudo-Newton method.

Provided insights into investment decisions under uncertainty.

Abstract

A nonlinear algebraic equation system of two variables is numerically solved, which is derived from a nonlinear algebraic equation system of four variables, that corresponds to a mathematical model related to investment under conditions of uncertainty. The theory of investment under uncertainty scenarios proposes a model to determine when a producer must expand or close, depending on his income. The system mentioned above is solved using a fractional iterative method, valid for one and several variables, that uses the properties of fractional calculus, in particular the fact that the fractional derivatives of constants are not always zero, to find solutions of nonlinear systems.