On the separation of solutions to fractional differential equations of order $α\in (1,2)$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909251181477888 |
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| author | Chaudhary, Renu Diethelm, Kai Hashemishahraki, Safoura |
| author_facet | Chaudhary, Renu Diethelm, Kai Hashemishahraki, Safoura |
| contents | Given the Caputo-type fractional differential equation $D^αy(t) = f(t, y(t))$ with $α\in (1, 2)$, we consider two distinct solutions $y_1, y_2 \in C[0,T]$ to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference $|y_1(t) - y_2(t)|$ for $t \in [0,T]$. The main emphasis is on describing how such bounds are related to the differences of the associated initial values. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_14771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the separation of solutions to fractional differential equations of order $α\in (1,2)$ Chaudhary, Renu Diethelm, Kai Hashemishahraki, Safoura Classical Analysis and ODEs 34A08, 34A12, 33E12 Given the Caputo-type fractional differential equation $D^αy(t) = f(t, y(t))$ with $α\in (1, 2)$, we consider two distinct solutions $y_1, y_2 \in C[0,T]$ to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference $|y_1(t) - y_2(t)|$ for $t \in [0,T]$. The main emphasis is on describing how such bounds are related to the differences of the associated initial values. |
| title | On the separation of solutions to fractional differential equations of order $α\in (1,2)$ |
| topic | Classical Analysis and ODEs 34A08, 34A12, 33E12 |
| url | https://arxiv.org/abs/2401.14771 |