Fractional shares are still eligible for dividends, but they’ll be proportional to the amount you own. For example, if you hold 0.5 shares of Apple, you’ll receive 50% of the dividend. Note: this won’t apply if the amount is too small (we can’t pay a fraction of a cent, for example).
The same logic applies for stock splits. If you hold 0.5 shares in Apple and the stock goes through a 2:1 split, you’ll now own 1 full share.
Please note however: your fractional shares are not transferable to another broker. If you close your account your fractional shares will need to be sold.