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

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.

Keywords

• Nonoscillation
• Dynamic equations
• Conformable derivative
• Riccati technique
• Time scale