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Asymptotic behavior and a new comparison technique for solutions of delta fractional difference equations

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  • Mohammed, Pshtiwan Othman
  • Arab, Meraa

Abstract

The paper introduces a novel comparison technique for fractional difference equations of delta-type, which is used to establish sharp criteria for the asymptotic behavior of their solutions. It is demonstrated that the Mittag-Leffler function emerges as the unique solution to a specific case of the proposed model. In addition, using the comparison theorem, we derive precise conditions under which solutions either diverge to infinity or converge to zero. These theoretical results provide a robust framework for analyzing the long-term dynamics of discrete fractional systems. Finally, to verify the main theorems numerically and demonstrate their practical implications, four illustrative examples are presented.

Suggested Citation

  • Mohammed, Pshtiwan Othman & Arab, Meraa, 2026. "Asymptotic behavior and a new comparison technique for solutions of delta fractional difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017758
    DOI: 10.1016/j.chaos.2025.117761
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