Oscillation Criteria of a Class of Fractional Order Damped Difference Equations

Abstract

Herein, we examine the oscillatory behavior of all solutions of a fractional order difference equations with damping term of the forms) and ∆ α denotes the Riemann-Liouville difference operator of order 0 < α ≤ 1. We arrive at some new sufficient conditions for the oscillation of solutions of fractional order damped difference equations using generalized riccati type transformation technique under suitable conditions.

Oscillation Analysis for Nonlinear Discrete Fractional Order Delay and Neutral Equations with Forcing Term

“…Recently, many researchers have shown interest in the study of oscillatory and non-oscillatory solutions of various types of fractional order difference equations (see [2,5,6,11,12,14,18,19,29]).…”

Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term

“…Of late, the investigation of the oscillation of solutions for fractional order difference equations has accelerated with several articles (see [21][22][23][24][25][26][27][28][29]). In what follows, we state some lemmas and preliminaries that will contribute in proving our main results.…”

Oscillation Theorems for Certain Forced Nonlinear Discrete Fractional Order Equations

“…Ever since Kuttner (for details, see [20]) mentioned the fractional order differences for the first time in 1956, the theory of difference equations of fractional order has been evolving (for details, see [1], [3], [8], [15], [17]). In recent years, the investigation of qualitative properties of discrete fractional equations has risen to prominence, with the study of oscillation of solutions of fractional difference equations drawing the interest of many researchers (for details, see [6], [11], [12], [13], [14], [24] and the references therein). Recently paper [21] dealt with the oscillatory properties of certain nonlinear fractional nabla difference equations of the form…”