SAMS Subject Classification Number: 5

The Riemann-Stieltjes integral was established from the works of Riemann and Steiltjes and has been recognized as a more generalized Riemann integral. This integral has opened doors for more theories and applications in the last decades. However, a differential operator associated with this integral has not been defined in the last decades. Very recently, by extending the concept of rate of change, a more general differential operator was suggested. Using the fundamental theorem of calculus, this operator was found to be the derivative associated with the Riemann-Stieltjes integral. In this talk, we present some new theoretical results and applications related to this extension.