import pandas as pd

def get_available_volume(start, end, security_name, volume_info):
    """
    Interpolate the volume of start trading and end trading time based on the volume information.
    Returns the difference as the available volume.

    Parameters:
    - start (datetime): Start time for availability calculation.
    - end (datetime): End time for availability calculation.
    - security_name (str): Name of the security for which to calculate availability.
    - volume_info (DataFrame): DataFrame containing trading volumes for different securities.

    Returns:
    - float: Available volume between start and end times.
    """
    stage = volume_info[volume_info['SecurityName'] == security_name]
    
    # Ensure datetimes are in a compatible format
    if isinstance(start, pd.DatetimeIndex):
        start = start.values[0]
    if isinstance(end, pd.DatetimeIndex):
        end = end.values[0]

    start_n_time = stage[(stage['TradingTimeEST'] >= start) & (stage['TradingTimeEST'] <= end)]['TradingTimeEST'].min()
    start_n_value = stage[stage['TradingTimeEST'] == start_n_time]['RemainingVolume'].values[0]
    
    # Interpolate available volume
    if pd.to_datetime(start).year != pd.to_datetime(stage['StartTradingTimeEST']).iloc[0].year:
        raise ValueError("Start time is not within the trading period.")
    if pd.to_datetime(end).year != pd.to_datetime(stage['EndTradingTimeEST']).iloc[-1].year:
        raise ValueError("End time is not within the trading period.")

    start_interpolate_value = stage[(stage['StartTradingTimeEST'] <= start) & (stage['EndTradingTimeEST'] >= start)][
        'RemainingVolume'].values[0] - stage[(stage['StartTradingTimeEST'] < start) & (stage['EndTradingTimeEST'] > start)][
        'RemainingVolume'].values[0]
    end_interpolate_value = stage[(stage['StartTradingTimeEST'] <= end) & (stage['EndTradingTimeEST'] >= end)][
        'RemainingVolume'].values[0] - stage[(stage['StartTradingTimeEST'] < end) & (stage['EndTradingTimeEST'] > end)][
        'RemainingVolume'].values[0]

    # Calculate available volume using interpolation
    if pd.to_datetime(start).year != pd.to_datetime(stage['StartTradingTimeEST']).iloc[0].year:
        raise ValueError("Start time is not within the trading period.")
    if pd.to_datetime(end).year != pd.to_datetime(stage['EndTradingTimeEST']).iloc[-1].year:
        raise ValueError("End time is not within the trading period.")

    available_volume = (end - start) / (pd.to_datetime(stage['EndTradingTimeEST']).iloc[0] - pd.to_datetime(stage['StartTradingTimeEST']).iloc[0]) * (
                stage[(stage['StartTradingTimeEST'] <= end) & (stage['EndTradingTimeEST'] >= end)][
                    'RemainingVolume'].values[0] - start_interpolate_value) + start_interpolate_value

    return available_volume

# Define the trading volume dataframes and times
volume_curve = pd.DataFrame({
    'SecurityName': ['GOOGL', 'APPL'],
    'TradingTimeEST': ['2016-03-22 09:00:00', '2016-03-22 10:00:00'],
    'RemainingVolume': [100, 200]
})

trading_time = pd.DataFrame({
    'SecurityName': ['GOOGL', 'APPL'],
    'EndTradingTimeEST': ['2016-03-22 11:30:00', '2016-03-22 12:30:00'],
    'StartTradingTimeEST': ['2016-03-22 09:15:00', '2016-03-22 10:15:00']
})

# Ensure datetimes are in a compatible format
volume_curve['TradingTimeEST'] = pd.to_datetime(volume_curve['TradingTimeEST'])
trading_time['StartTradingTimeEST'] = pd.to_datetime(trading_time['StartTradingTimeEST'])
trading_time['EndTradingTimeEST'] = pd.to_datetime(trading_time['EndTradingTimeEST'])

# Calculate available volume
available_volume_googol = get_available_volume(
    start=pd.to_datetime('2016-03-22 09:50'),
    end=pd.to_datetime('2016-03-22 11:15'),
    security_name=['GOOGL'],
    volume_info=volume_curve
)

print(f"Available Volume for Google: {available_volume_googol} barrels")