Analysis of the maps with variable fractional order
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912228778704896 |
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| author | Gade, Prashant M. Bhalekar, Sachin Chevala, Janardhan |
| author_facet | Gade, Prashant M. Bhalekar, Sachin Chevala, Janardhan |
| contents | Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear variable order difference equations where the order is periodic function with period $T$. We give a general procedure for arbitrary $T$ and for $T=2$ and $T=3$, we give exact results. For $T=2$, we find that the lower order determines the stability of the equations. For odd $T$, numerical simulations indicate that we can approximately determine the stability of equations from the mean value of the variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of the maps with variable fractional order Gade, Prashant M. Bhalekar, Sachin Chevala, Janardhan Dynamical Systems 26A33, 39A30 Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear variable order difference equations where the order is periodic function with period $T$. We give a general procedure for arbitrary $T$ and for $T=2$ and $T=3$, we give exact results. For $T=2$, we find that the lower order determines the stability of the equations. For odd $T$, numerical simulations indicate that we can approximately determine the stability of equations from the mean value of the variables. |
| title | Analysis of the maps with variable fractional order |
| topic | Dynamical Systems 26A33, 39A30 |
| url | https://arxiv.org/abs/2502.07290 |