To answer your question, "Fractals" and the "alligator" are nothing more than fancy terms for displaced moving averages and support/resistance zones made obvious by low, lower low, lowest low, higher low, higher low & vice versa. I recommend looking at our Friendlytrend Signal indicator on here to help a bit. However, keep in mind there's nothing magical other than helping determine overall trend.
Our method that we use for our trend analysis and filtering involves looking across daily, weekly, and monthly timeframes for holding positions for a few weeks to a year. If you're using the Alligator (we prefer a bit different moving avg), look for consistently up or down across all three timeframes. This alone will help you if you want to trend follow. If the trend is upward, look to use a fractal support zone at least 2-5% of the downside as a trailing stop point. The same goes for downtrends but in reverse.
Don't overcomplicate it. Also, we always look at fundamentals to support our investment/trading decisions in technical trends. Technical trends without fundamental basis is a quick way to lose.