There are 2 methods to deduct car expenses as an independent contractor.
You can use the standard mileage rate method. This is around 55 cents per mile (it changes each year) and covers all your car expenses including fuel, maintenance, repairs, and wear and tear. To use this method you must have accurate records of the: date, time, mileage driven and business purpose of each trip. (Uber may provide this in the app.)
Or you can use the actual expense method. You need the same mileage records, plus you need the total of all miles driven in the year (business plus personal), plus you need records of all your car expenses (gas, maintenance, repairs). You can include depreciation (wear and tear) and lease payments if the vehicle is leased. You are allowed to deduct the percentage of expenses that equals your percentage of business use. (For example, if you drove 20,000 miles and 12,000 miles was for Uber, you could deduct 60% of your actual expenses.)
The IRS will expect that you have accurate business records and be able to prove your expenses if audited; the IRS does not have to allow any deduction you can't prove.
If you track your fuel purchases in an app, or accounting software like Quicken or Mint, but don't keep the actual receipts, then it will be up to the auditor. If your business records are generally in good order, they may allow the fuel expense even without receipts, but it depends on the person and how they are feeling that day. If your records are sloppy and not well kept, they may not allow any expense without a receipt.
See more specifically chapter 4 here https://www.irs.gov/pub/irs-pdf/p463.pdf
