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

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

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 i...

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Main Authors: A. George Maria Selvam, Jehad Alzabut, Mary Jacintha, Abdullah Özbekler
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/5495873
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spelling doaj-78042db691764258b4b651741280ddbb2020-11-25T03:26:59ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/54958735495873Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping TermA. George Maria Selvam0Jehad Alzabut1Mary Jacintha2Abdullah Özbekler3Department of Mathematics, Sacred Heart College, Tirupattur, -635601 Tamil Nadu, IndiaDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh -11586, Saudi ArabiaDepartment of Mathematics, Sacred Heart College, Tirupattur, -635601 Tamil Nadu, IndiaDepartment of Mathematics, Atilim University, 06830, Incek, Ankara, TurkeyThe 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.http://dx.doi.org/10.1155/2020/5495873
collection DOAJ
language English
format Article
sources DOAJ
author A. George Maria Selvam
Jehad Alzabut
Mary Jacintha
Abdullah Özbekler
spellingShingle A. George Maria Selvam
Jehad Alzabut
Mary Jacintha
Abdullah Özbekler
Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
Journal of Function Spaces
author_facet A. George Maria Selvam
Jehad Alzabut
Mary Jacintha
Abdullah Özbekler
author_sort A. George Maria Selvam
title Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
title_short Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
title_full Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
title_fullStr Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
title_full_unstemmed Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
title_sort oscillation results for a class of nonlinear fractional order difference equations with damping term
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/5495873
work_keys_str_mv AT ageorgemariaselvam oscillationresultsforaclassofnonlinearfractionalorderdifferenceequationswithdampingterm
AT jehadalzabut oscillationresultsforaclassofnonlinearfractionalorderdifferenceequationswithdampingterm
AT maryjacintha oscillationresultsforaclassofnonlinearfractionalorderdifferenceequationswithdampingterm
AT abdullahozbekler oscillationresultsforaclassofnonlinearfractionalorderdifferenceequationswithdampingterm
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