Can I book airline tickets online on my credit card for travel within USA by my relatives?

Will they have any problems since the tickets would have been purchased from my credit card and I am not travelling with them?
Will they need to show who has purchased tickets for them?
If yes, how do they prove their relation with me?
What documents should they carry for their personal identification?
What documents should be carried by an adult student from India who doesn't possess a credit or debit card?

if they have hard copies of the tickets it doesn't matter who purchased the tickets. Corporations and businesses constantly purchase tickets for their employees and the same thing happens with individuals. So long as the ticket is in the person who is using the tickets name no problem. They must have a picture ID and if they are traveling internationally they should have their passport and current visa for the country of destination. good luck

Most online purchases through airline websites do require the credit card holder to be one of the people traveling when making an online purchase and receiving an e-ticket and ask that the credit card be presented when checking in. Almost all websites do not give you the option of receiving a paper ticket. What you might do is to search for fares on the internet and then call the airline to explain the situation and make the arrangements for paper tickets on the phone. They will charge a nominal fee for the paper tickets and mailing. but will solve the problem of you not being amongst the traveling party and the associated issues. Another option is to purchase the tickets through a travel agent.