The results of continuous fertilization during 40 years indicated increases of all forms phosphorus in the soil except of phosphorus bound to calcium and organic phosphorus. Application of higher amounts of P-fertilizer resulted in the dominance of the Al–P fraction in the studied soil, which indicated that this fraction was the most

responsible for the migration of phosphorus along the soil profile. Excerpts from Fractionation of soil phosphorus in a long-term phosphate fertilization .. Some relevant PDFs enclosed 

 I think the fractionation scheme is dependent on the soil pH, weathering, calcareous and O.M%. The original fractionation procedures and the most important modifications were summarized by Kuo (1996).

Kuo, S. 1996. Phosphorus. In: D.L. Sparks (ed.) Methods of soil analysis. Agronomy 9. ASA-SSSA, Madison, WI.

I recommend you to view of below file as PDF.

I think Hedley"s procedure still holds good

What is the purpose of the fractionation?

There are several methods for P fractionation depends upon your interest as mentioned above by Paul Milham. i.e. if you want to know the organic and inorganic type along with apatite and non-apatite then you can use Standard Measurement and Testing (SMT) method. If you are interested in bonding type i.e. strong and weak then you can see Sequential extraction method and if you interested for P association with different elements i.e. Al, Fe, Ca then you can use Psenner method. 

Hope it will help. 

The reference'Methods of P Analysis'  edited by Pierzynski is worth consulting (suggested by Dr.Ahmad).Chapter  on Phosphorus fractionation by Zhang,H. and Kover,J.L. page 50 onwards provides the methods of fractionation with  brief review.One can choose the method based on purpose of study and objective.

@Paul Milham Sir purpose of Fractionation is to check the Long term effects of Nitrogen and Phosphorus fertlization on P fractions..

It appears to me that the Jiang and Gu P fractionation was developed for calcareous soils by further modifying the original Chang and Jackson,1957 fractionation scheme.Ca -P was further fractionated in to di, octa and apatite P forms.I could see only summary and the original paper is in Chinese.If the soil is calcareous and if one desires to study the chemical nature of accumulated P ,the Jiang and Gu fractionation can be followed.If the purpose is interpretation of P fractionation data interms of plant availablity,then Hedley's fractionation is better option.Using Hedley's fractionation one can also interpret the P availablity from organic P pools.