As per Muslim Law (Shariat), a Muslim can dispose of by will only 1/3rd of his property which is left after payment of his funeral expenses, death bed charges, debts owed by him, expenses for obtaining probate or letters of administration or succession certificate, etc. Hence, subject to the above condition vesting of the property fully in one of your sons will be valid. Your other sons cannot object to the vesting of the entire property in favor of one of them, as under Islamic law all properties belong to the person whether earned by him or inherited from his father or G father or gifted to him etc and there is no right to any of his children or wife unless conferred by the person by gift or sale etc.
As regards the applicability of Muslim Personal Law (Shariat), The Muslim Personal Law (Shariat) Application Act, 1937 provides that Shariat shall apply notwithstanding any custom or usage to the contrary in all questions relating to intestate succession, special property of females, etc. The Act requires that a declaration in the prescribed form shall be filed with the prescribed authority declaring that he wants to obtain the benefits of the Act. Once the declaration is filed all his children and their descendants will be governed by the Shariat.