A Note on Various Special Calculations Between the Ramp Function and Caputo-type Derivatives

Abstract: This special note provides preliminary information on the ramp (signal) function, which plays a significant role in engineering and science, and offers advantages for the efficient use of various computer-aided programs in different types of (mathematical) computations. Following this, we will present the fundamentals of certain Caputo-type calculations, which are also associated with a form of fractional calculus of arbitrary order. Furthermore, several specific computations involving the Caputo-type derivatives of the ramp function will be performed, and the key results obtained from these computations will be discussed.