Behavior of solutions of higher-order difference equations

Badriah S. Alofi; Abdulaziz S. Alofi; Badriah S. Alofi; Abdulaziz S. Alofi

doi:10.3934/math.2026555

AIMS Mathematics

2026, Volume 11, Issue 5: 13485-12499. doi: 10.3934/math.2026555

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Behavior of solutions of higher-order difference equations

Badriah S. Alofi ^{1
,
,},
Abdulaziz S. Alofi ²

1.
Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received: 11 January 2026 Revised: 20 April 2026 Accepted: 07 May 2026 Published: 14 May 2026
MSC : 39A10

This paper examined a new class of difference equations, focusing on the stability, boundedness, and periodicity of solutions. Special cases admitting explicit solutions wrere also considered. Numerical examples were provided to confirm the theoretical results and illustrate the consistency between analytical predictions and computational observations. These findings contributed to a deeper understanding of the qualitative behavior of discrete-time dynamical systems and offered insight into the dynamics of higher-order difference equations.
- difference equation,
- stability,
- boundedness,
- solution of difference equation
Citation: Badriah S. Alofi, Abdulaziz S. Alofi. Behavior of solutions of higher-order difference equations[J]. AIMS Mathematics, 2026, 11(5): 13485-12499. doi: 10.3934/math.2026555

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Abstract

This paper examined a new class of difference equations, focusing on the stability, boundedness, and periodicity of solutions. Special cases admitting explicit solutions wrere also considered. Numerical examples were provided to confirm the theoretical results and illustrate the consistency between analytical predictions and computational observations. These findings contributed to a deeper understanding of the qualitative behavior of discrete-time dynamical systems and offered insight into the dynamics of higher-order difference equations.

References

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