We reviewed the concept of classical differential operator with its history, development, and its use at the end of the first chapter. As such, we looked into how this idea has been essential in calculus and calculus-based applications. At the tail-end of the chapter, we offered an extension of this classical notion-the derivative of one function with respect to another. It was a natural evolution-to deepen the comprehension of differential operators in more intricate situations. Following this framework, the present chapter seeks to widen the field of fractional differential equations, well-known in numerous areas for the ability of modeling behaviors that classical differential equations struggle to reproduce. This covers the fractional derivativeDerivative concept itself, specifically in relation to these derivatives with respect to another function for many kernelsKernel. Through the exploration of different types of these fractional derivatives, we will, at the same time, point out their power to generalize classical derivatives, accommodating a more general framework for tackling more complex equations. Furthermore, in this chapter, we will show how fractional derivatives enable to recover some well-known classical differential operators when conditions are satisfied and the appropriate functions are chosen. This will greatly contribute to the theoretical understanding of the fractional calculus, whilst facilitating modeling of complex systems in physical, biological, and engineering domains exhibiting memory, non-local, and non-linear interactions and efforts.