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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Oscillatory Properties of Fractional-Order Partial Difference Equations with Boundary Conditions

Journal of Applied Nonlinear Dynamics 15(4) (2026) 979--989 | DOI:10.5890/JAND.2026.12.012

R. Dhineshbabu$^{1}$, R. Janagaraj$^{2}$, A. George Maria Selvam$^{3}$, D. Abraham Vianny$^{4}$

$^{1}$ Department of Science and Humanities, R.M.K. College of Engineering and Technology (Autonomous), Thiruvallur- 601206, Tamil Nadu, India

$^{2}$ Department of Mathematics, Faculty of Engineering, Karpagam Academy of Higher Education, Coimbatore- 641021, Tamil Nadu, India

$^{3}$ Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur - 635 601, Tamil Nadu, India

$^{4}$ Department of Mathematics, IFET College of Engineering (Autonomous), Gangarampalayam, Villupuram- 605108, Tamil Nadu, India

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Abstract

This work establishes new sufficient conditions that ensure all solutions are oscillatory for a class of forced nonlinear fractional partial difference equations. A key contribution of this study is the distinction between two types of boundary conditions: inhomogeneous conditions, which introduce external influences through boundary terms, and homogeneous damping-type conditions, which regulate the solution internally. These boundary conditions play a central role in shaping the qualitative behavior of solutions. The analysis is carried out using the Riemann-Liouville fractional difference operator of order $\eta\in(0,1]$, together with forcing terms that influence the system's dynamics. The results extend existing oscillation criteria to a broader class of nonlinear problems. Numerical examples are provided to illustrate and validate the theoretical findings.

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