Work

Riccati technique and nonoscillation of damped linear dynamic equations with the conformable derivative on time scales

Year: 2025

Type: article

Abstract: In this study, we investigate the use of damped linear dynamic equations with the conformable derivative on time scales to provide sufficient conditions to guarantee nonoscillation for nontrivial solutions of both ordinary differential and discrete equations. The nonoscillation theorem is proven using the Riccati technique, and we provide four examples to explain nonoscillation. The four examples include the damped Euler-type dynamic equation on a time scale, the q -difference equation, and the forward difference and ordinary differential equations with periodic coefficients . In particular, the ordinary differential equation with periodic coefficients is inspired by Whittaker–Hill’s equation, which has applications in the theory of internal rotation in the hydrogen peroxide molecule.

Source: Results in Applied Mathematics

DOI: 10.1016/j.rinam.2025.100553

Author: Kazuki Ishibashi

Institution: Hiroshima Institute of Technology

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,770

Funder: Japan Society for the Promotion of Science