Fractional Order Calculus and Derivative Implementation

Abstract

The concept of fractional calculus dates  back to the early days of calculus and may be traced back  to Arbogast's publications in the 1800s. Multiple  derivatives are defined in this situation by powers of D that  are logically discovered to be integral in nature. However,  this gave birth to the idea of evaluating this operator's  fractional power and attempting to determine its equivalent  form or operating it on some function in a meaningful  way.This part of calculus is classified as special calculus,  and it did not find much application in engineering until  the advent of electronic computers and control systems,  where it began to show its capability, such as increasing  the number of control parameters in a PID control system,  which essentially increases its ability to be optimised,  albeit at a higher complexity. This project begins with  introducing the fundamentals of fractional calculus,  followed by fractional derivatives of standard functions  and their interpretation, and then provides fractional  calculus applications in the context of electronics.