Question

which one is superceed the other? laplace or Fourier transform

Answer 1

Depends on use.
Laplace is a time domain transformation
Fourier is a frequency domain transformation

Answer 2

IN LAPLACE TRANSFORM THERE IS CONCEPT OF REGION OF CONVERGENCE BUT IN FOURIER TRANSFORM THERE IS NO CONCEPT OF REGION OF CONVERGENCE. AS S=(SIGMA +JW) IN LAPLACE TRANSFORM BUT IN FOURIER TRANSFORM WE PUT SIGMA=0(THIS IS THE MOST IMPORTANT DIFFERENCE) .REGION OF CONVERGENCE IS VALUE OF SIGMA FOR WHICH LAPLACE INTEGRAL CONVERGES.THIS IS THE MAIN ADVANTAGE OF LAPLACE TRANSFORM OVER FOURIER TRANSFORM