Abstract
<jats:p>This chapter provides a comprehensive exploration of Caputo-Fabrizio fractional derivatives, detailing their theoretical foundations and practical applications. It begins with the properties and definitions of the Caputo-Fabrizio derivative, followed by an analysis of its applications to polynomial, exponential, and trigonometric functions. The discussion encompasses the existence and uniqueness of solutions for fractional differential equations involving this derivative, as well as various numerical schemes designed for their resolution. Additionally, the chapter contrasts integer-order growth models with fractional-order models, highlighting the advantages of fractional derivatives in capturing complex dynamics. A significant application in cancer modeling is also presented, demonstrating the potential of Caputo-Fabrizio derivatives to enhance our understanding of tumor growth dynamics and bridging theoretical concepts with the practical implementations.</jats:p>