Yes, explanatory statement may be required in the case of special resolution if and only if such business is a special business.
Thus criteria of judging whether explanatory statement is required or not is the nature of business. If business is special business then in that case explanatory statement is mandatory.
As per Section 173 (1) (a) there are 4 ordinary business. In an AGM only these four businesses are ordinary business rest all are special businesses.
In case of any other general meeting like EGM all business are special business
4 are ordinary business are as follows:
(i) the consideration of the accounts, balance sheet and the reports of the Board of directors and auditors, (ii) the declaration of a dividend, (iii) the appointment of directors in the place of those retiring, and (iv) the appointment of, and the fixing of the remuneration of, the auditors.