Initial value problem for a class of semi-linear fractional iterative differential equations. (English) Zbl 07924342
Summary: An initial value problem of a class of semi-linear fractional order iterative differential equations is researched in this paper. The existence of solution is acquired in respect of Banach space \(C(I, I)\) and \(C_{K, q}(I, I)\) for fractional order iterative differential equations. Nevertheless, because the operator is Hölder continuous rather than Lipschitz continuous, uniqueness results can not be obtained. Additionally, a change of solution to \([k, \beta]\) for the \(k\in I\) will arise from a small perturbation of the initial value. Our analysis is on the basis of the properties of Mittag-Leffler function and Schauder’s fixed point theorem. Lastly, some examples are provided to demonstrate our results.
MSC:
| 26A33 | Fractional derivatives and integrals |
| 33E12 | Mittag-Leffler functions and generalizations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
Keywords:
fractional order iterative differential equations; Mittag-Leffler function; initial value problem; existenceReferences:
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