Fractional-Order Non-linear Nabla Difference Equation via Hilfer-Type Operator: Oscillation Results
摘要
This chapter explores the oscillatory behavior, a qualitative aspect, of solutions to the nonlinear fractional difference equation that utilizes the Hilfer-type nabla fractional difference operator. Our approach differs significantly from existing literature, based on the Riccati methodology, combined with recently developed discrete fractional calculus techniques and mathematical inequalities. This strategy is built on more reliable estimations, allowing us to derive new, less stringent conditions that guarantee the oscillation of every solution to the nonlinear Hilfer-type nabla fractional difference equation. Our results enhance the understanding of how the Hilfer-type nabla fractional-order difference operator affects the oscillation behavior of the associated fractional difference equation. Additionally, we present two numerical simulations at the end of the paper to illustrate the practical implications of our findings.