Volterra Integral Equation

An integral equation in which the integration domain depends on the independent variable, typically of the form x(t)=f(t)+∫_{a}^{t} K(t,s)x(s) ds (Volterra of the second kind) or ∫_{a}^{t} K(t,s)x(s) ds=f(t) (first kind), embodying causal or history-dependent coupling.