Further Research for Lagrangian Mechanics within Generalized Fractional Operators-Reference-Cited by-同舟云学术

Further Research for Lagrangian Mechanics within Generalized Fractional Operators

Published:2023-05-23 Issue:6 Volume:7 Page:421
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Song Chuanjing¹

Affiliation:

1. School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China

Abstract

In this article, the problems of the fractional calculus of variations are discussed based on generalized fractional operators, and the corresponding Lagrange equations are established. Then, the Noether symmetry method and the perturbation to Noether symmetry are analyzed in order to find the integrals of the equations. As a result, the conserved quantities and the adiabatic invariants are obtained. Due to the universality of the generalized fractional operators, the results achieved here can be used to solve other specific problems. Several examples are given to illustrate the universality of the methods and results.

Funder

National Natural Science Foundation of China

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/6/421/pdf

Reference66 articles.

1. Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Integrals and Derivatives—Theory and Applications, John Wiley and Sons Inc.

2. Podlubny, I. (1999). Fractional Differential Equations, Academic Press.

3. Wu, Q., and Huang, J.H. (2016). Fractional Order Calculus, Tsinghua University Press.

4. Unique continuation for fractional orders of elliptic equations;Yu;Ann. PDE,2017

5. A fractional Dirac equation and its solution;Muslih;J. Phys. A Math. Theor.,2010