Oscillation theorems for nonlinear fractional difference equations

Abstract

In this study, we discuss some theorems related to the oscillatory behavior of nonlinear fractional difference equations equipped with well-known fractional Riemann-Liouville difference operator. Then we give an example for the illustration of the results obtained.

Oscillation criterion for Euler type half‐linear difference equations

“…To complete the literature overview, we add the research papers below as well as the books [1, 32], where fundamental results from the oscillation theory of linear and half‐linear difference equations are mentioned. Concerning the oscillation of linear difference equations, we refer to [33–40] (see also [41–48] for other relevant criteria about more general equations). The oscillation theory of perturbed difference equations is analyzed in [49, 50] (see also [51]).…”

A Survey on the Oscillation of Solutions for Fractional Difference Equations

“…Motivated by the above works, Adiguzel [29,30] considered the oscillation behavior of the solutions of the following delta fractional difference equations:…”

Existence and oscillation results for the Hybrid generalized pantograph Hilfer fractional difference equation

“…Oscillation is a crucial aspect of applied mathematics and can be created or removed by the inclusion of nonlinearity, delay or a stochastic term. The oscillation of differential and difference equations opens up a wide range of practical applications, including torsional oscillations, periodic oscillations, voltagecontrolled neuron theories and harmonic oscillation with damping; see, e.g., the papers [3,12,13,16,29,30] for more details. In [19], Grace et al introduced and examined the oscillation of fractional differential equations.…”