Generalized fractional operators for nonstandard Lagrangians

TL;DR

This paper explores how generalized fractional operators can be applied to nonstandard Lagrangians, especially in dissipative systems, revealing diverse motion configurations through analysis of Euler-Lagrange and Hamilton equations.

Contribution

It introduces the use of generalized fractional operators in nonstandard Lagrangians, expanding the modeling capabilities for dissipative systems.

Findings

Different motion configurations can be obtained via the generalized kernel.

The approach provides a flexible framework for analyzing dissipative systems.

Examples demonstrate the applicability of the method.

Abstract

In this note we study the application of generalized fractional operators to a particular class of nonstandard Lagrangians. These are typical of dissipative systems and the corresponding Euler-Lagrange and Hamilton equations are analyzed. The dependence of the equation of motion on the generalized kernel permits to obtain a wide range of different configurations of motion. Some examples are discussed and analyzed.