Voice Culture - Working on Vocal range
Mandra Sadhna:
One thing you can try is Madra Sadhna i.e, the more you sing and sustain each swara of lower octave, it increases your range itself allowing you to sing in higher notes.
Starting from Madhya Shadj (i.e., Sa of Middle Octave). Take a deep breath and sustain the Sa, try making it more and more stable. Practice it for few minutes, this is called 'Sa bharna'.
Now move on to Mandra Nishad (i.e., Ni of Lower Octave). Sustain it for 2 or 3 deep breaths. Move on to Mandra Dhaivat (dha), Pancham (Pa), Madyam (Ma) and so on as per your reach as a beginner. Then in similar fashion move back towards Madhya Shadj (Sa).
Practicing it everyday you will realise that singing lower octave notes becomes more and more easy. And it increases your reach towards those lower notes which you were not able to sing earlier. Moreover it improves your higher octave too, surprising it may seem, but its real effective practice.
Basic Alankar or Palta:
Other thing you can do is, take some alankar, practice it till taar Sa. Once your voice starts gaining command over the swar and speed, you can go higher in the same alankar like till taar Re or Ga. This will help you to sing higher range swaras.
Start with simple,
sa re ga ma pa dha ni sa' ni dha pa ma ga re sa ; singing each swara in one matra (beat) and the whole sequence repeatedly.
Moving on to,
sa re ga ma pa dha ni sa' re' sa' ni dha pa ma ga re sa ;
Following the same till Taar Gandhar (ga' of higher octave), Taar Madhyam and so on.
This technique can be applied to any alankar or palta,
sa re ga, re ga ma, ga ma pa, ma pa dha, pa dha ni, dha ni sa' , sa' ni dha, ni dha pa, dha pa ma, pa ma ga, ma ga re, ga re sa
And then extending it till taar re' ,
sa re ga, re ga ma, ga ma pa, ma pa dha, pa dha ni, dha ni sa' , ni sa' re' , re' sa' ni, sa' ni dha, ni dha pa, dha pa ma, pa ma ga, ma ga re, ga re sa
And so on.
Moreover, as we are practicing these patterns while singing one swara in one matra (one note per beat). After gaining control over notes, we can start singing 2 swaras in one matra (2 notes per beat). With practice it can later be done in 4 notes per beat as well. And this can be mastered over TIME only and requires DEDICATION :)
If any confusion, you can approach me for help.