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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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    References listed on IDEAS

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    1. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    2. Abdeljawad, Thabet, 2018. "Different type kernel h−fractional differences and their fractional h−sums," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 146-156.
    3. Almusawa, Musawa Yahya & Mohammed, Pshtiwan Othman, 2023. "Approximation of sequential fractional systems of Liouville–Caputo type by discrete delta difference operators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    5. Pshtiwan Othman Mohammed & Ravi P. Agarwal & Majeed A. Yousif & Eman Al-Sarairah & Alina Alb Lupas & Mohamed Abdelwahed, 2024. "Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting," Mathematics, MDPI, vol. 12(18), pages 1-16, September.
    6. Wang, Mei & Jia, Baoguo & Chen, Churong & Zhu, Xiaojuan & Du, Feifei, 2020. "Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    7. Pshtiwan Othman Mohammed & Hari Mohan Srivastava & Nejmeddine Chorfi & Majeed A. Yousif & Dumitru Baleanu & Shrooq Mohammed Azzo, 2025. "Solutions comparative for a novel model of fractional delta difference type," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 31(1), pages 2482560-248, December.
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