Y-function and L'Hospital-type Monotonicity Rules with Nabla and Diamond-Alpha Derivatives on Time Scales

TL;DR

This paper develops new monotonicity rules using Y-functions and L'Hospital-type criteria for nabla and diamond-alpha derivatives within the framework of time scales calculus.

Contribution

It introduces novel monotonicity rules involving Y-functions and L'Hospital-type criteria specifically for nabla and diamond-alpha derivatives on time scales.

Findings

Established Y-function monotonicity rules on time scales.

Formulated L'Hospital-type monotonicity rules for nabla and diamond-alpha derivatives.

Unified approach to monotonicity in dynamic equations on time scales.

Abstract

The main objective of this paper is to establish the $Y$-function and L'Hospital-type monotonicity rules with nabla and diamond-alpha derivatives on time scales.