INITIAL VALUE PROBLEM FOR A CLASS OF SEMI-LINEAR FRACTIONAL ITERATIVE DIFFERENTIAL EQUATIONS

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, I ) and C K,q ( I, I ) for fractional order iterative differential equations. Nevertheless, because the operator is Ho<spacing diaeresis>lder continuous rather than Lipschitz continuous, uniqueness results can not be obtained. Additionally, a change of solution to [ k, beta ] for the k is an element of 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.