Stability Analysis of Higher Order Fractional Difference Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914417459855360 |
|---|---|
| author | Chevala, Janardhan Bhalekar, Sachin |
| author_facet | Chevala, Janardhan Bhalekar, Sachin |
| contents | Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear difference equations $Δ^α x(t) + a \, Δ^β x(t+α-β-1) =(b-1)x(t+α-2)$. The stability results are derived, and we discuss the bifurcations for $0<β\leq 1 < α\leq 2$, $a>0$, $b \in \mathbb{C}$ or $b \in \mathbb{R}$ with examples. We extend this to the stability of an equilibrium point of a nonlinear higher-order fractional difference equation. Moreover, we study the stability of higher-order one-term linear fractional difference equations $Δ^α x(t) = (c-1) x(t+α-N)$ with $N-1<α\leq N$, where $N \in \mathbb{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23090 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability Analysis of Higher Order Fractional Difference Equations Chevala, Janardhan Bhalekar, Sachin Dynamical Systems 39A30, 39A28, 26A33 Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear difference equations $Δ^α x(t) + a \, Δ^β x(t+α-β-1) =(b-1)x(t+α-2)$. The stability results are derived, and we discuss the bifurcations for $0<β\leq 1 < α\leq 2$, $a>0$, $b \in \mathbb{C}$ or $b \in \mathbb{R}$ with examples. We extend this to the stability of an equilibrium point of a nonlinear higher-order fractional difference equation. Moreover, we study the stability of higher-order one-term linear fractional difference equations $Δ^α x(t) = (c-1) x(t+α-N)$ with $N-1<α\leq N$, where $N \in \mathbb{N}$. |
| title | Stability Analysis of Higher Order Fractional Difference Equations |
| topic | Dynamical Systems 39A30, 39A28, 26A33 |
| url | https://arxiv.org/abs/2603.23090 |