Oscillation theorems for damped fractional order difference equations

In this paper, we present a systematic study concerning the developments of the oscillation results for the fractional difference equations. Essential preliminaries on discrete fractional calculus are stated prior to giving the main results. Oscillation results are presented in a subsequent order and for different types of equations. The investigation was carried out within the delta and nabla operators.

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“…Selvam et al [34,35] examined the new oscillation criteria for forced delta fractional nonlinear difference equations of the form:…”

Section: Corollary 2 ([33]mentioning

confidence: 99%

“…then Equation (32) is oscillatory. 35) and (36) hold for some constant K 1 > 0, then Equation (32) is oscillatory. 35) and (36) hold for some constant K 2 > 0, then Equation (32) is oscillatory.…”

Section: Corollary 6 ([40]mentioning

confidence: 99%

A Survey on the Oscillation of Solutions for Fractional Difference Equations

et al. 2022

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“…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]).…”

Section: Introductionmentioning

confidence: 99%

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

Selvam¹,

Alzabut²,

Janagaraj³

et al. 2020

DSA

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Selvam

Alzabut

Jacintha

et al. 2020

Journal of Function Spaces

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The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Δψλzηλ+pλzηλ+qλF∑s=λ0λ−1+μ λ−s−1−μys=0, where zλ=aλ+bλΔμyλ, Δμ stands for the fractional difference operator in Riemann-Liouville settings and of order μ, 0<μ≤1, and η≥1 is a quotient of odd positive integers and λ∈ℕλ0+1−μ. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.

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Oscillation theorems for damped fractional order difference equations

Cited by 11 publications

References 7 publications

A Survey on the Oscillation of Solutions for Fractional Difference Equations

A Survey on the Oscillation of Solutions for Fractional Difference Equations

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

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

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