The theory of quaternionic operators has applications in several different fields, such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and quaternionic operator theory is based on the definition of a spectrum. In fact, in quaternionic operator theory the classical notion of a resolvent operator and the one of a spectrum need to be replaced by the two S-resolvent operators and the S-spectrum. This is a consequence of the noncommutativity of the quaternionic setting. Indeed, the S-spectrum of a quaternionic linear operator T is given by the noninvertibility of a second order operator. This presents new challenges which make our approach to perturbat...