Research of the hereditary dynamic Riccati system with modification fractional differential operator of Gerasimov-Caputo

TL;DR

This paper investigates a fractional Riccati differential equation with a variable order Gerasimov-Caputo operator, applying Newton's method to analyze solutions and assess numerical accuracy improvements.

Contribution

It introduces a modified fractional operator in Riccati equations and evaluates a numerical algorithm's accuracy using Newton's method and the Runge rule.

Findings

Numerical solutions are constructed for various parameters.

Computational accuracy improves with finer grid nodes.

The method's accuracy approaches theoretical limits as nodes increase.

Abstract

In this paper, we study the Cauchy problem for the Riccati differential equation with constant coefficients and a modified Gerasimov-Caputo type fractional differential operator of variable order. Using Newton's numerical algorithm, calculation curves are constructed taking into account different values of the Cauchy problem parameters. The calculation results are compared with the previously obtained results. The computational accuracy of the numerical algorithm is investigated. It is shown using the Runge rule that the computational accuracy tends to the accuracy of the numerical method when increasing the nodes of the calculated grid.