I applied Inverse Fourier transform in my equation but it is giving me same output. Please tell me how to solve this particular equation.
It looks like your function goes to infinity as omega goes to infinity.
Mathematica does not give an answer to this one either:
InverseFourierTransform[\[Omega]^(1/4), \[Omega], t]
although it does for InverseFourierTransform[\[Omega], \[Omega], t] and for InverseFourierTransform[\[Omega]^2, \[Omega], t]. Anyone is expert in Fourier transforms of distributions?
Is there any way to solve this kind of equation.