Vitamin D deficiency has been shown to be prevalent in people with fatigue, and correction of the deficiency improves the fatigue- "Results:

Prevalence of low vitamin D was 77.2% in patients who presented with fatigue. After normalization of vitamin D levels fatigue symptom scores improved significantly (P < 0.001) in all five subscale categories of fatigue assessment questionnaires.

Conclusion:

The prevalence of low vitamin D is high in patients who present with fatigue and stable chronic medical conditions, if any. Normalization of vitamin D levels with ergocalciferol therapy significantly improves the severity of their fatigue symptoms." https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4158648/

Of not also is that the researchers used ergocalciferol, the synthetic D2 form which is less effective than the cholecalciferol D3 form - https://www.ncbi.nlm.nih.gov/pubmed/15531486 https://www.ncbi.nlm.nih.gov/pubmed/21177785