Research Article Oscillation of Third-Order Nonlinear Generalized Difference Equation with Multiple Neutral Terms M. Sumathy , 1 P. Venkata Mohan Reddy, 1 M. Maria Susai Manuel, 1 and M. Syed Ali 2 1 Department of Science and Humanities, R M D Engineering College, Kavaraipettai 601 206, ndia 2 Department of Mathematics, Tiruvalluvar University, Vellore, Tamil Nadu, ndia CorrespondenceshouldbeaddressedtoM.Sumathy;ks.snh@rmd.ac.in Received 2 September 2022; Revised 22 October 2022; Accepted 8 November 2022; Published 29 December 2022 AcademicEditor:LeonidShaikhet Copyright©2022M.Sumathyetal.TisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Inthispaper,theauthorsdiscusstheoscillatorybehaviourofathirdordergeneralizeddiferenceequationwithmultipleneutral terms.WehavealsoappliedRiccatitransformationandPhilotypetechniquetoderivenewoscillationcriteriaforthediference equation in question. Suitable examples are provided to validate our main results. 1. Introduction Te theory of diference equations has grown immensely overthepastfewdecades.Inthe feldof probability theory, statistical analysis, combinatorial analysis, electrical net• works, and sociology, diference equations has emerged as mathematical models describing real life challenges. In the recent past, the study of oscillation and non• oscillation for second order nonlinear diference equations has garnered a great deal of attention [1, 2]. Te latest re• search also emphasizes the diferent kinds of diference equations,includingordinary,linear,nonlinear,superlinear, quasilinear, sublinear, delay, and neutral delay diference equations. Interestingly, one can refer the oscillatory be• havior for sublinear neutral delay second and third order diference equations in [3, 4]. An investigation of the os• cillation of the second•order quasilinear neutral delay dif• ference equations can be seen in [5, 6]. Te study of the Oscillation of second order half•linear diference equations has also been given in [7]. Importantly, the oscillation criteriaforhigherorderneutralequationscanbeseenin[8]. Te literature regarding the present study is referred in [9, 10]. In a revealing manner, tracking a maneuvering target, and fault diagnosis of wind turbine gearbox is per• formed in [11] by using the properties of Riccati diference equation.In[12],forthestudyoftheMittag•Lefer stability analysisoffractionaldiscretetimeneuralnetworks,aclassof semilinear fractional diference equations are used. A few applications of specifc kinds of nonlinear third orderdelaydiferenceequationsareprominentinthestudy ofMathematicalBiology,Economics,andmanyother felds of Mathematics that involve discrete models [13–16]. Moreover,oscillatorysolutionofthirdorderdelaydiference equations are used to remove speckle noise in the feld of image processing which can be seen in [17]. Te suitable smoothingflter fortheedgemaskcomputedusingthethird order diference equation is examined in [18]. Our main focus in this paper is on the oscillatory be• haviorofthethird•orderdiferenceequations.Intheearlier research,plethoraofmethodsabouttheoscillatoryproperty of third order diference equation were presented. For in• stance, in [19] the third order diference equation under consideration is as follows: Δ a ξ Δ b ξ Δx ξ     + q ξ fx ξ− m+1   � h ξ , ξ ≥ ξ 0 , (1) where a ξ ,b ξ ,q ξ  are positive real sequences, m is positive integer, f ∈ C(R, R) with uf(u) > 0 for u ≠ 0 and  ∞ ξ�ξ 0 1/a ξ �  ∞ ξ�ξ 0 1/b ξ � ∞. Using the Riccati transforma• tion technique, sufcient conditions for the existence of oscillatory solutions are provided. In [20], the authors considered the following equation: Hindawi Mathematical Problems in Engineering Volume 2022, Article ID 8103094, 13 pages https://doi.org/10.1155/2022/8103094