Oscillatory and Asymptotic Criteria for a Fifth-Order Fractional Difference Equation

Abstract

In this paper, using the properties of the conformable fractional difference and fractional sum, we initially establish some oscillatory and asymptotic criteria for a fifth-order fractional difference equation. Several critical inequalities, the Riccati transformation technique, and the integral technique are used in the deduction process. We provide some example to test the results. The established criteria are new results in the study of oscillation, and can be extended to other types of high-order fractional difference equations as well as fractional differential equations with more complicated forms.