Work

The Euler-Lagrange equations of nabla derivatives for variational approach to optimization problems on time scales

Year: 2024

Type: article

Abstract: This paper investigates the variational approach using nabla (denoted as ∇ ) within the framework of time scales. By employing two different methods, we derive the Euler-Lagrange equations for first-order variational approach to optimization problems involving exponential functions, as well as for those with both exponential functions and their ∇ -derivatives. To establish the high-order variational approach to optimization problem, we present the Leibniz Formula for ∇ -derivatives along with its proof. Additionally, we determine the high-order variational approach to optimization problem incorporating ∇ -derivatives of exponential functions. Through these analyses, we aim to contribute to the understanding and application of the variational calculus on time scales, offering insights into the behavior of dynamic systems governed by exponential functions and their derivatives.

Source: Advances in Continuous and Discrete Models

DOI: 10.1186/s13662-024-03832-5

Authors: Jie Bai, Zhijun Zeng

Institutions: Liaoning University, Northeast Normal University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,790

Funder: People's Government of Jilin Province