The Cotangent Derivative with Respect to Another Function: Theory, Methods and Applications

This paper introduces a generalization of the Riemann–Liouville and Caputo cotangent derivatives and their corresponding integrals, known as the Riemann–Liouville and Caputo cotangent derivatives with respect to another function (RAF). These fractional derivatives possess the advantageous property of forming a semigroup. The paper also presents a collection of theorems and lemmas, providing solutions to linear cotangent differential equations using the generalized Laplace transform. Moreover, we present the numerical approach, the application for solving the Caputo cotangent fractional Cauchy problem, and two examples for testing this approach.