On Fredholm partial integro-differential equation of the third order

We study single-valued solvability of the initial value problem for a nonlinear partial Fredholm integro-differential equation of the third order with degenerate kernel. First we modify a method of degenerate kernel of partial Fredholm integro-differential equation of the second kind to the case of Fredholm integro-differential equations of the third order. After solving the corresponding system of algebraic equations we obtain the Volterra integral equation of the second kind. Further we use the method of successive approximations combined with the method of contractive mappings.