An old fashion way that some singers are taught to hold notes is to sing in a cold bath or a cold shower. Or better yet go into a pool or beach but don't let it be so cold that you may freeze to death or become ill and try to sing a hard song there preferably by Mariah Carey or Whitney Houston. Then sing a solfedge or do ABCs going higher in notes each letter by using a piano if you can and find out what your limit is and try to exceed that limit each time you rehearse. What this does is that it may strain your body a bit but it should eventually teach you how to sustain a note.
Notice the difference between your head voice and your chest voice. Mariah can sing and shift between both which can give her much more range but her falsettos and higher notes are used with her head voice. When you release notes, always keep in mind that you should keep warm air as much as possible while breathing out from your diaphragm. Try singing Me - May - Mah- Mo- Moo in notes: C-E-G-E-C (on instrument or notes; there are virtual keyboards online if you don't have an instrument) Then replace the Me-May-Mah-Mo-Moo with "Hee" sounds. Do the "Hee" with warm air in the CEGEC ranges going up the scales in octaves. By octaves, this is the set of a range. Mariah Carey has a 6-7 octave range which helps her attain all the notes she sings in her song, not just necessarily, "My All." Mariah Carey herself has stated previously that she has been able to hit notes that she can no longer do. So the basic key lesson is to maintain singing in long ranges up and down the scales and octaves and holding out the notes as much as you can.
Stand up with your feet spread apart aligning with your shoulders, up straight but not so stiff so your knees are a bit relaxed. Now push out "hee" with warm air and add sound. Now go up and down the scale with HEE, HUH, HO, HA, HEE. This is a breathing excercise to push out the vocal ability of sustaining. And when you hold it out, you can also tell what kind of vibrato you naturally have if you can get it to flow naturally.
Lower notes tend to be thicker, richer in volume so you have to push more with deep sound singing from your chest voice which is close to what you use for your natural talking voice but you have to sing it. Higher notes are airy, more lighter but louder so your upper mouth palette has much to do with this so raise it it up a a bit, slight open your mouth, breathe out the fastest warm air and push from your diaphram the notes you need work on.
Avoid caffeine, alcohol, and cold water as this can tighten the vocal chords. You may want just water, honey, and natural ingredients for your throat so it will be properly lubricated. Also when you sing, it helps to record it and keep track of which notes precisely you need to work on.