Any equation for an unknown function involving integrals and derivatives of the function. Many different types can arise and there is no straightforward classification. The initial-value problem (see ordinary differential equations) given by
f′(x) = F(x,f(x),∫xaK(x,y) f(y) dy)
f(a) = f0
also contains features common to Volterra integral equations (see integral equation). Boundary-value problems and equations involving partial derivatives also occur in practice.