Many classic forms were adapted in the 20th century. New ones were invented.
Messiaen's musical world is amazing. Check what intervals are the best for him to build a cadence!
Regarding the sonata, he says: "having written some absolutely regular sonata-allegros, we shall state that one thing in that form has become obsolete: the recapitulation. Then we shall try once more to keep what is most essential: the development. there are two in a sonata-allegro: the middle, modulating development; the terminal development, generally built over understood dominant and tonic pedals. We shall be able to write pieces made of this terminal development alone".
And he gives this example from les Enfants de Dieu (from la Nativité du Seigneur):
First element over a dominant pedal in B major and development
A great fortissimo cry upon a sort of schema with augmentation of the theme
A tender phrase, forming the conclusion, established over a tonic pedal in B major.
You can hear this part here:
In his writings, he gives additional examples of this kind of technique and new "free forms proceeding from the development of the sonata-allegro".
Some thoughts about all this:
Having in mind that tonality in Messiaen cannot be understood in strictly classic ways, he uses a contemporary technique (as Debussy did) to establish tonal centers and a relationship between them: the pedal tone.
It's interesting how Messiaen is not interested at all in parts without development, ruling out at first glance the recapitulation ("obsolete") because it has no modulation nor development.
It's also interesting how he takes only a section (or better said, the concept of a section) of the sonata-allegro, to build up his own coherent form. In my opinion, this is related to the big idea in Messiaen of "progressive music": non retrogradable rhythms or added values, non transposable modes... All of them have to be with that idea on not allowing the music to fall in the repetition patterns where classic music had rely on.
This is just an example of what Messiaen did with forms. He talks about fugue, an other forms he was interested in, some of them fresh and new (Bird son), some old (plainchant).
Is this concept interesting for you?
For me, it is. It opens more possibilities of organising music material.