Oscillatory Properties of Fractional-Order Partial Difference Equations with Boundary Conditions
DOI:
https://doi.org/10.5890/JAND.2026.12.012Abstract
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.References
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