2020
DOI: 10.1515/ms-2017-0422
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Oscillation criteria for a class of nonlinear discrete fractional order equations with damping term

Abstract: The aim in this work is to investigate oscillation criteria for a class of nonlinear discrete fractional order equations with damping term of the form$$\begin{array}{} \displaystyle \Delta\left[a(t)\left[\Delta\left(r(t)g\left(\Delta^\alpha x(t)\right)\right)\right]^\beta\right]+p(t)\left[\Delta\left(r(t)g\left(\Delta^\alpha x(t)\right)\right)\right]^\beta+F(t,G(t))=0, t\in N_{t_0}. \end{array}$$In the above equation α (0 < α ≤ 1) is the fractional order, $\begin{array}{} \displaystyle G(t)=\sum\limits_{s=t… Show more

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Cited by 6 publications
(3 citation statements)
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“…Chatzarakis et al [36] examined the oscillatory behavior for a class of nonlinear delta fractional difference equations with the damping term of the form: (22) where 0 < ν ≤ 1; c 4 , r 7 , q 9 : [t 0 , ∞) → R + are continuous sequences with c 4 (t) > q 9 (t); γ 5 ≥ 1 is a quotient of two odd positive integers; for the continuous function…”
Section: Corollary 2 ([33]mentioning
confidence: 99%
“…Chatzarakis et al [36] examined the oscillatory behavior for a class of nonlinear delta fractional difference equations with the damping term of the form: (22) where 0 < ν ≤ 1; c 4 , r 7 , q 9 : [t 0 , ∞) → R + are continuous sequences with c 4 (t) > q 9 (t); γ 5 ≥ 1 is a quotient of two odd positive integers; for the continuous function…”
Section: Corollary 2 ([33]mentioning
confidence: 99%
“…Recently, many researchers have come up with new findings in the study on the oscillatory and nonoscillatory behaviour solutions of difference equations/fractional order difference equations (see [4], [10], [11], [13], [14], [19], [21], [27], [29]).…”
Section: Some Significant Previous Workmentioning
confidence: 99%
“…By using Riemann Liouville calculus, Riccati transformation, and inequality methods, the vibration analysis of even number neutral differential equations was achieved. Reference [6] proposed an oscillation analysis method based on nonlinear fractional order differential equations with damping terms. This algorithm utilizes Riemann Liouville calculus, Riccati transformation, and inequality methods to obtain sufficient conditions for the oscillation of nonlinear fractional differential equations with damping terms.…”
Section: Introductionmentioning
confidence: 99%