<p>A newly developed framework for a fractional derivative operator involving a non-singular generalized exponential kernel, along with its singular kernel extension, was introduced recently. This paper is devoted to the study of fractional Riccati equations with exponential extension kernel derivatives. In addition to the newly proposed fractional derivative, the investigation also considers two well-known non-singular fractional derivatives, namely the Caputo-Fabrizio and Atangana-Baleanu models. We study the existence and uniqueness of solutions to initial value problems defined by fractional Riccati equations with the considered exponential extension kernel derivatives. Subsequently, numerical algorithms are proposed and developed to obtain approximate solutions for the studied problems using these derivatives. The main objective of this paper is to assess the impact of the selected exponential extension kernel formulations on the dynamics of the fractional Riccati equations.</p>