Your required "88 ~ 1057 HZ" frequency is a low pitched audio tone.
The FM broadcast band is from 88Mhz to 108MHz, a million times higher.
You can make an adjustable voltage with a pre-set resistor and apply the voltage to a vari-cap diode in the transmitter's oscillator. The voltage changes the capacitance of the vari-cap which changes the RF frequency.
Since the modulation in FM occurs by changing the RF frequency, a vari-cap diode can also be the modulator.
Here is an example of a fairly high power FM transmitter that uses a pot to adjust the RF frequency and the vari-cap for modulation: