You can use the Pattern and Matcher class, I wrote a quick code it should be clear (subtracting 32 from an ascii alphabetical lower case char will give you its upper case, see the ascii table).
String s = "Anthony";
Pattern pattern = Pattern.compile("[aeiou]");
Matcher matcher = pattern.matcher(s);
String modifiedString = "";
while(matcher.find())
{
modifiedString = s.substring(0, matcher.start()) + (char)(s.charAt(matcher.start()) - 32) + s.substring(matcher.end());
}
System.out.println(modifiedString);