Generalized perturbation equation for integral and integro-differential equations and applications

Following the idea of [1], a generalized perturbation equation is proposed for integral and integro-differential equations to study contraction and stability properties of solutions not representable by a formula. This opens new avenues for theoretical and numerical investigation of behaviour of solutions without explicitly solving those equations. Applications are considered to Abelʹs equation and to nonlinear Volterra integral and integro-differential equations yielding interesting and practically important contractivity and stability results.