| Volume 14, Number 5, 2024, Pages - DOI：10.11948/JAAC-2023-0353 |
| Initial value problem for a class of semi-linear fractional iterative differential equations |
| Mi Zhou,Lu Zhang |
| Keywords:fractional oder iterative differential equations · Mittag-Leffler function · initial value problem · existence |
| Abstract: |
| An initial value problem of a class of semi-linear fractional order iterative differential equations is studied in this paper. The existence of solution for fractional order iterative differential equations is obtained in Banach space $C(J,J)$ and $C_{K,\alpha}(J,J)$ respectively. However, uniqueness results can not be acquired since the operator only is H\"{o}lder continuous but not Lipschitz continuous. Furthermore, a small perturbation of the initial value will cause a change in the solution on $[k,b]$ for the $k\in J$. Our analysis is based on Schauder"s fixed point theorem and the properties of Mittag-Leffler function.
Finally, an example is given to illustrate our results. |
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