LEIBNIZ RULE, THE CHAIN RULE, AND TAYLOR’S THEOREM FOR FRACTIONAL DERIVATIVES

摘要

This paper is directed toward that end. Here three elementary formulas from the calculus arc generalized to include fractional derivatives:(1) the Leibniz rule for the derivative of the product of two functions, (2) the chain rule for the derivative of a composite function, and (3) Taylor's theorem for the expansion of a function in a power series. Each of the three generalized results is applied to the study of the special functions of math metical physics. New relations among these functions, and simpler derivations of known results arc obtained.