Op-Amp variable pulse generator
THis will easily work with dual supply .

But use Pot for R to change frequency from 1k to 10K using fixed 1k R in series with 10k Pot and C=0.1uF

The  Positive feedback is simply equal R values from output to Mid-supply (V+ +V-)/2 = 0V in this case.

This changes the threshold of the Relaxation Oscillation just like CMOS Schmitt triggers with 50% Hysteresis for the sawtooth input voltage on the Vin- RC side. to switch outputs.

The  negative feedback R self biases the cap to cross the upper and lower Vin+ threshold switched bu the output.

Interactive Falstad Simulation here



Your design adjusts the duty cycle.

This design rises 50% duty cycle and adjusts frequency by  RC=T rise time approx. 50% vs T@ 63%. R is shown as a fixed R but has a soft slider on right to adjust from slider option 1k to 10k. OK?

I also used a single supply, so I used Pull-up/down to get V+/2 with equal R equivalent values. I set Vout to only swing 2 to 10V from Vcc=12V due to some Saturation values of the driver . just approx.  OK?

For a dual supply use equal R's and remove pullup R to V+.