How can I solve this Volterra integral equation of the second kind?

Question

I would like to solve an integral equation that I believe to be a Volterra integral equation of the second kind. I don't know how to solve it and I am not used to solve integral equations.

$$\hat{P}(k) = \int_{0}^{k} dq K(k,q) \hat{P}(q)$$ with $K(k,q) = \frac{ \beta}{k^{\beta}}q^{\beta - 1} e^{-\frac{k^2 \alpha(\frac{q}{k})}{2}}$

and $\alpha(U) = \frac{D}{\mu^3}\left[4U - U^2 -2ln(U) - 3 \right]$

Beta, mu and D are real positive constant. P hat is the Fourier transform of P, symmetric in k. P is a symmetric probability density function.

Do you have an idea on how to tackle this resolution ?

Any help would be appreciated,

Thanks